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Multiple linear regression

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Ken Plummer

The document discusses multiple linear regression and partial correlation. It explains that multiple regression allows one to analyze the unique contribution of predictor variables to an outcome variable after accounting for the effects of other predictor variables. Partial correlation similarly examines the relationship between two variables while controlling for a third, but only considers two variables, whereas multiple regression examines the effects of multiple predictor variables simultaneously. Examples are given comparing the correlation between height and weight with and without controlling for other relevant variables like gender, age, exercise habits, etc.

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What is a Multiple Linear Regression?
Welcome to this learning module on Multiple Linear Regression
In this presentation we will cover the following aspects of Multiple Regression:
In this presentation we will cover the following aspects of Multiple Regression: - Connection to Partial Correlation and ANCOVA
In this presentation we will cover the following aspects of Multiple Regression: - Connection to Partial Correlation and ANCOVA - Unique contribution of each variable
In this presentation we will cover the following aspects of Multiple Regression: - Connection to Partial Correlation and ANCOVA - Unique contribution of each variable - Contribution of all variables at the same time
In this presentation we will cover the following aspects of Multiple Regression: - Connection to Partial Correlation and ANCOVA - Unique contribution of each variable - Contribution of all variables at the same time - Type of data multiple regression can handle
In this presentation we will cover the following aspects of Multiple Regression: - Connection to Partial Correlation and ANCOVA - Unique contribution of each variable - Contribution of all variables at the same time - Type of data multiple regression can handle - Types of relationships multiple regression describes
In this presentation we will cover the following aspects of Multiple Regression: - Connection to Partial Correlation and ANCOVA - Unique contribution of each variable - Contribution of all variables at the same time - Type of data multiple regression can handle - Types of relationships multiple regression describes
In this presentation we will cover the following aspects of Multiple Regression: - Connection to Partial Correlation and ANCOVA - Unique contribution of each variable - Contribution of In all this variables presentation at the we same will time - Type of data multiple cover the regression concept of can Partial handle Correlation. - Types of relationships multiple regression describes
In this presentation we will cover the following aspects of Multiple Regression: - Connection to Partial Correlation and ANCOVA - Unique contribution of each variable - Contribution of all variables at the same time - Type of data multiple regression can handle - Types of relationships multiple regression describes After going through this presentation look at the presentation on Analysis of Covariance and consider what multiple regression and ANCOVA have in common.
In this presentation we will cover the following aspects of Multiple Regression: - Connection to Partial Correlation and ANCOVA - Unique contribution of each variable - Contribution of What all variables is a Partial at Correlation? the same time - Type of data multiple regression can handle - Types of relationships multiple regression describes
Partial correlation estimates the relationship between two variables while removing the influence of a third variable from the relationship.
Like in the example that follows,
Like in the example that follows, a Pearson Correlation between height and weight would yield a .825 correlation.
Like in the example that follows, a Pearson Correlation between height and weight would yield a .825 correlation. We might then control for gender (because we think being female or male has an effect on the relationship between height and weight).
However, when controlling for gender the correlation between height and weight drops to .770.
However, when controlling for gender the correlation between height and weight drops to .770. Individual Height (inches) Weight (pounds) Sex (1 – male, 2 – female) A 73 240 1 B 70 210 1 C 69 180 1 D 68 160 1 E 70 150 2 F 68 140 2 G 67 135 2 H 62 120 2
However, when controlling for gender the correlation between height and weight drops to .770. Individual Height (inches) Weight (pounds) Sex (1 – male, 2 – female) A 73 240 1 B 70 210 1 C 69 180 1 D 68 160 1 E 70 150 2 F 68 140 2 G 67 135 2 H 62 120 2
However, when controlling for gender the correlation between height and weight drops to .770. Individual Height (inches) Weight (pounds) Sex (1 – male, 2 – female) A 73 240 1 B 70 210 1 C 69 180 1 D 68 160 1 E 70 150 2 F 68 140 2 G 67 135 2 H 62 120 2 &
However, when controlling for gender the correlation between height and weight drops to .770. Individual Height (inches) Weight (pounds) Sex (1 – male, 2 – female) A 73 240 1 B 70 210 1 C 69 180 1 D 68 160 1 E 70 150 2 F 68 140 2 G 67 135 2 H 62 120 2 &
However, when controlling for gender the correlation between height and weight drops to .770. Individual Height (inches) Weight (pounds) Sex (1 – male, 2 – female) A 73 240 1 B 70 210 1 C 69 180 1 D 68 160 1 E 70 150 2 F 68 140 2 G 67 135 2 H 62 120 2 & controlling for
However, when controlling for gender the correlation between height and weight drops to .770. Individual Height (inches) Weight (pounds) Sex (1 – male, 2 – female) A 73 240 1 B 70 210 1 C 69 180 1 D 68 160 1 E 70 150 2 F 68 140 2 G 67 135 2 H 62 120 2 & controlling for
However, when controlling for gender the correlation between height and weight drops to .770. Individual Height (inches) Weight (pounds) Sex (1 – male, 2 – female) A 73 240 1 B 70 210 1 C 69 180 1 D 68 160 1 E 70 150 2 F 68 140 2 G 67 135 2 H 62 120 2 & controlling for = .770
This is very helpful because we may think two variables (height and weight) are highly correlated but we can determine if that correlation holds when we take out the effect of a third variable (gender).
While in partial correlation, only two variables are correlated while holding a third variable constant, in multiple regression several variables are grouped together to predict an outcome variable.
While in partial correlation, only two variables are correlated while holding a third variable constant, in multiple regression several variables are grouped together to predict an outcome variable Independent or Predictor Variables
While in partial correlation, only two variables are correlated while holding a third variable constant, in multiple regression several variables are grouped together to predict an outcome variable Independent or Predictor Variables Height
While in partial correlation, only two variables are correlated while holding a third variable constant, in multiple regression several variables are grouped together to predict an outcome variable Independent or Predictor Variables Height Gender
While in partial correlation, only two variables are correlated while holding a third variable constant, in multiple regression several variables are grouped together to predict an outcome variable Independent or Predictor Variables Height Gender Age
While in partial correlation, only two variables are correlated while holding a third variable constant, in multiple regression several variables are grouped together to predict an outcome variable Independent or Predictor Variables Height Gender Age Soda Drinking
While in partial correlation, only two variables are correlated while holding a third variable constant, in multiple regression several variables are grouped together to predict an outcome variable Independent or Predictor Variables Height Gender Age Soda Drinking Exercise
While in partial correlation, only two variables are correlated while holding a third variable constant, in multiple regression several variables are grouped together to predict an outcome variable Independent or Predictor Variables Height Gender Age Soda Drinking Exercise Dependent, Response or Outcome Variable
While in partial correlation, only two variables are correlated while holding a third variable constant, in multiple regression several variables are grouped together to predict an outcome variable Independent or Predictor Variables Height Gender Age Soda Drinking Exercise Dependent, Response or Outcome Variable Weight
While in partial correlation, only two variables are correlated while holding a third variable constant, in multiple regression several variables are grouped together to predict an outcome variable Independent or Predictor Variables Height Gender Age Soda Drinking Exercise Dependent, Response or Outcome Variable Weight all have an influence on . . .
While in partial correlation, only two variables are correlated while holding a third variable constant, in multiple regression several variables are grouped together to predict an outcome variable Independent or Predictor Variables Height Gender Age Soda Drinking Exercise Dependent, Response or Outcome Variable Weight all have an influence on . . .
While in partial correlation, only two variables are correlated while holding a third variable constant, in multiple regression several variables are grouped together to predict an outcome variable Independent or Predictor Variables Height Gender Age Soda Drinking Exercise Dependent, Response or Outcome Variable Weight all have an influence on . . .
While in partial correlation, only two variables are correlated while holding a third variable constant, in multiple regression several variables are grouped together to predict an outcome variable Independent or Predictor Variables Height Gender Age Soda Drinking Exercise Dependent, Response or Outcome Variable Weight all have an influence on . . .
While in partial correlation, only two variables are correlated while holding a third variable constant, in multiple regression several variables are grouped together to predict an outcome variable Independent or Predictor Variables Height Gender Age Soda Drinking Exercise Dependent, Response or Outcome Variable Weight all have an influence on . . .
While in partial correlation, only two variables are correlated while holding a third variable constant, in multiple regression several variables are grouped together to predict an outcome variable Independent or Predictor Variables Height Weight Gender Age Soda Drinking Exercise Dependent, Response or Outcome Variable all have an influence on . . .
In this presentation we will cover the following aspects of Multiple Regression: - Connection to Partial Correlation and ANCOVA - Unique contribution of each variable - Contribution of all variables at the same time - Type of data multiple regression can handle - Types of relationships multiple regression describes
Essentially, the group of predictors are all covariates to each other. Independent or Predictor Variables Height Weight Gender Age Soda Drinking Exercise Dependent, Response or Outcome Variable all have an influence on . . .
Meaning, Independent or Predictor Variables Height Weight Gender Age Soda Drinking Exercise Dependent, Response or Outcome Variable all have an influence on . . .
Meaning, for example, Independent or Predictor Variables Height Weight Gender Age Soda Drinking Exercise Dependent, Response or Outcome Variable all have an influence on . . .
Meaning, for example, that it is possible to identify the unique prediction power of height on weight Independent or Predictor Variables Height Weight Gender Age Soda Drinking Exercise Dependent, Response or Outcome Variable all have an influence on . . .
Meaning, for example, that it is possible to identify the unique prediction power of height on weight Independent or Predictor Variables Gender Age Soda Drinking Exercise Dependent, Response or Outcome Variable all have an influence Height on . . . Weight
Meaning, for example, that it is possible to identify the unique prediction power of height on weight after you’ve taken out the influence of all of the other predictors. Independent or Predictor Variables Gender Age Soda Drinking Exercise Dependent, Response or Outcome Variable all have an influence Height on . . . Weight
Meaning, for example, that it is possible to identify the unique prediction power of height on weight after you’ve taken out the influence of all of the other predictors. Independent or Predictor Variables Gender Age Soda Drinking Exercise Dependent, Response or Outcome Variable all have an influence Height on . . . Weight
For example, Independent or Predictor Variables Height Weight Gender Age Soda Drinking Exercise Dependent, Response or Outcome Variable all have an influence on . . .
For example, here is the correlation between Height and Weight without controlling for all of the other variables. Independent or Predictor Variables Gender Age Soda Drinking Exercise Dependent, Response or Outcome Variable all have an influence Height on . . . Weight
For example, here is the correlation between Height and Weight without controlling for all of the other variables. Independent or Predictor Variables Gender Age Soda Drinking Exercise Dependent, Response or Outcome Variable all have an influence Height on . . . Weight Correlation = .825
However, Independent or Predictor Variables Height Weight Gender Age Soda Drinking Exercise Dependent, Response or Outcome Variable all have an influence on . . .
However, here is the correlation between Height and Weight after taking out the effect of all of the other variables. Independent or Predictor Variables Height Weight Gender Age Soda Drinking Exercise Dependent, Response or Outcome Variable all have an influence on . . .
However, here is the correlation between Height and Weight after taking out the effect of all of the other variables. Independent or Predictor Variables Gender Age Soda Drinking Exercise Dependent, Response or Outcome Variable all have an influence on . . . Weight Height
However, here is the correlation between Height and Weight after taking out the effect of all of the other variables. Independent or Predictor Variables Gender Age Soda Drinking Exercise Dependent, Response or Outcome Variable all have an influence Height on . . . Weight Correlation = .601
However, here is the correlation between Height and Weight after taking out the effect of all of the other variables. Independent or Predictor Variables Gender Age Soda Drinking Exercise Dependent, Response or Outcome Variable all have an influence on . . . Weight Correlation = .601 So, after eliminating the effect of gender, age, soda, and exercise on weight, the unique correlation that height shares with weight is .601. Height
Even though we were only correlating height and weight when we computed a correlation of .825,
Even though we were only correlating height and weight when we computed a correlation of .825, the other four variables still had an influence on weight.
Even though we were only correlating height and weight when we computed a correlation of .825, the other four variables still had an influence on weight. However, that influence was not accounted for and remained hidden.
With multiple regression we can control for these four variables and account for their influence
With multiple regression we can control for these four variables and account for their influence thus calculating the unique contribution height makes on weight without their influence being present.
We can do the same for any of these other variables. Like the relationship between Gender and Weight.
We can do the same for any of these other variables. Like the relationship between Gender and Weight. Independent or Predictor Variables Height Age Soda Drinking Exercise Dependent, Response or Outcome Variable all have an influence on . . . Weight Gender
We can do the same for any of these other variables. Like the relationship between Gender and Weight. Independent or Predictor Variables Height Age Soda Drinking Exercise Dependent, Response or Outcome Variable all have an influence on . . . Weight Gender Correlation = .701
But when you take out the influence of the other variables the correlation drops from .701 to .582.
BEFORE Independent or Predictor Variables Height Age Soda Drinking Exercise Dependent, Response or Outcome Variable all have an influence on . . . Weight Gender Correlation = .701
AFTER
AFTER Independent or Predictor Variables Height Age Soda Drinking Exercise Dependent, Response or Outcome Variable all have an influence on . . . Weight Gender
AFTER Independent or Predictor Variables Height Age Soda Drinking Exercise Dependent, Response or Outcome Variable all have an influence on . . . Weight Gender Correlation = .582
Here is the correlation between age and weight before you take out the effect of the other variables:
Here is the correlation between age and weight before you take out the effect of the other variables: Independent or Predictor Variables Height Gender Soda Drinking Exercise Dependent, Response or Outcome Variable all have an influence on . . . Age Weight
Here is the correlation between age and weight before you take out the effect of the other variables: Independent or Predictor Variables Height Gender Soda Drinking Exercise Dependent, Response or Outcome Variable all have an influence on . . . Age Weight Correlation = .435
The correlation drops from .435 to .385 after taking out the influence of the other variables:
The correlation drops from .435 to .385 after taking out the influence of the other variables: Independent or Predictor Variables Height Gender Soda Drinking Exercise Dependent, Response or Outcome Variable all have an influence on . . . Age Weight
The correlation drops from .435 to .385 after taking out the influence of the other variables: Independent or Predictor Variables Height Gender Soda Drinking Exercise Dependent, Response or Outcome Variable all have an influence on . . . Age Weight Correlation = .385
In this presentation we will cover the following aspects of Multiple Regression: - Connection to Partial Correlation and ANCOVA - Unique contribution of each variable - Contribution of all variables at the same time - Type of data multiple regression can handle - Types of relationships multiple regression describes
Beyond estimating the unique power of each predictor,
Beyond estimating the unique power of each predictor, multiple regression also estimates the combined power of the group of predictors.
Beyond estimating the unique power of each predictor, multiple regression also estimates the combined power of the group of predictors.
Beyond estimating the unique power of each predictor, multiple regression also estimates the combined power of the group of predictors. Independent or Predictor Variables Height Weight Gender Age Soda Drinking Exercise Dependent, Response or Outcome Variable
Beyond estimating the unique power of each predictor, multiple regression also estimates the combined power of the group of predictors. Independent or Predictor Variables Height Weight Gender Age Soda Drinking Exercise Dependent, Response or Outcome Variable Combined Correlation = .982
In this presentation we will cover the following aspects of Multiple Regression: - Connection to Partial Correlation and ANCOVA - Unique contribution of each variable - Contribution of all variables at the same time - Type of data multiple regression can handle - Types of relationships multiple regression describes
Multiple regression can estimate the effects of continuous and categorical variables in the same model.
Multiple regression can estimate the effects of continuous and categorical variables in the same model. Independent or Predictor Variables Height Dependent, Response or Outcome Variable Gender Age Soda Drinking Exercise Weight
Multiple regression can estimate the effects of continuous and categorical variables in the same model. Independent or Predictor Variables Height Height is represented by continuous data – because height can take on any value between two points in inches or centimeters. Dependent, Response or Outcome Variable Gender Age Soda Drinking Exercise Weight
Multiple regression can estimate the effects of continuous and categorical variables in the same model.
Multiple regression can estimate the effects of continuous and categorical variables in the same model. Independent or Predictor Variables Height Age Soda Drinking Exercise Dependent, Response or Outcome Variable all have an influence on . . . Weight Gender Gender is a represented by categorical data – because gender can take on two values (female or male)
In this presentation we will cover the following aspects of Multiple Regression: - Connection to Partial Correlation and ANCOVA - Unique contribution of each variable - Contribution of all variables at the same time - Type of data multiple regression can handle - Types of relationships multiple regression describes
Multiple regression can describe or estimate linear relationships like average monthly temperature and ice cream sales:
Multiple regression can describe or estimate linear relationships like average monthly temperature and ice cream sales: 700 600 500 400 300 200 100 0 0 20 40 60 80 100 120 Ave Monthly Temperature Average Monthly Ice Cream Sales
Multiple regression can describe or estimate linear relationships like average monthly temperature and ice cream sales: 700 600 500 400 300 200 100 0 0 20 40 60 80 100 120 Ave Monthly Temperature Average Monthly Ice Cream Sales
It can also describe or estimate curvilinear relationships.
For example,
For example, what if in our fantasy world the temperature reached 100 degrees and then 120 degrees. Let’s say with such extreme temperatures ice cream sales actually dip as consumers seek out products like electrolyte-enhanced drinks or slushies.
Then the relationship might look like this:
Then the relationship might look like this: 700 600 500 400 300 200 100 0 0 20 40 60 80 100 120 Ave Monthly Temperature Average Monthly Ice Cream Sales
Then the relationship might look like this: 700 600 500 400 300 200 100 0 0 20 40 60 80 100 120 Ave Monthly Temperature Average Monthly Ice Cream Sales This is an example of a Curvilinear Relationship
In summary,
In summary, Multiple Regression is like single linear regression but instead of determining the predictive power of one variable (temperature) on another variable (ice cream sales) we consider the predictive power of other variables (such as socio-economic status or age).
With multiple regression you can estimate the predictive power of many variables on a certain outcome,
With multiple regression you can estimate the predictive power of many variables on a certain outcome, as well as the unique influence each single variable makes on that outcome after taking out the influence of all of the other variables.

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Multiple linear regression

  • 1. What is a Multiple Linear Regression?
  • 2. Welcome to this learning module on Multiple Linear Regression
  • 3. In this presentation we will cover the following aspects of Multiple Regression:
  • 4. In this presentation we will cover the following aspects of Multiple Regression: - Connection to Partial Correlation and ANCOVA
  • 5. In this presentation we will cover the following aspects of Multiple Regression: - Connection to Partial Correlation and ANCOVA - Unique contribution of each variable
  • 6. In this presentation we will cover the following aspects of Multiple Regression: - Connection to Partial Correlation and ANCOVA - Unique contribution of each variable - Contribution of all variables at the same time
  • 7. In this presentation we will cover the following aspects of Multiple Regression: - Connection to Partial Correlation and ANCOVA - Unique contribution of each variable - Contribution of all variables at the same time - Type of data multiple regression can handle
  • 8. In this presentation we will cover the following aspects of Multiple Regression: - Connection to Partial Correlation and ANCOVA - Unique contribution of each variable - Contribution of all variables at the same time - Type of data multiple regression can handle - Types of relationships multiple regression describes
  • 9. In this presentation we will cover the following aspects of Multiple Regression: - Connection to Partial Correlation and ANCOVA - Unique contribution of each variable - Contribution of all variables at the same time - Type of data multiple regression can handle - Types of relationships multiple regression describes
  • 10. In this presentation we will cover the following aspects of Multiple Regression: - Connection to Partial Correlation and ANCOVA - Unique contribution of each variable - Contribution of In all this variables presentation at the we same will time - Type of data multiple cover the regression concept of can Partial handle Correlation. - Types of relationships multiple regression describes
  • 11. In this presentation we will cover the following aspects of Multiple Regression: - Connection to Partial Correlation and ANCOVA - Unique contribution of each variable - Contribution of all variables at the same time - Type of data multiple regression can handle - Types of relationships multiple regression describes After going through this presentation look at the presentation on Analysis of Covariance and consider what multiple regression and ANCOVA have in common.
  • 12. In this presentation we will cover the following aspects of Multiple Regression: - Connection to Partial Correlation and ANCOVA - Unique contribution of each variable - Contribution of What all variables is a Partial at Correlation? the same time - Type of data multiple regression can handle - Types of relationships multiple regression describes
  • 13. Partial correlation estimates the relationship between two variables while removing the influence of a third variable from the relationship.
  • 14. Like in the example that follows,
  • 15. Like in the example that follows, a Pearson Correlation between height and weight would yield a .825 correlation.
  • 16. Like in the example that follows, a Pearson Correlation between height and weight would yield a .825 correlation. We might then control for gender (because we think being female or male has an effect on the relationship between height and weight).
  • 17. However, when controlling for gender the correlation between height and weight drops to .770.
  • 18. However, when controlling for gender the correlation between height and weight drops to .770. Individual Height (inches) Weight (pounds) Sex (1 – male, 2 – female) A 73 240 1 B 70 210 1 C 69 180 1 D 68 160 1 E 70 150 2 F 68 140 2 G 67 135 2 H 62 120 2
  • 19. However, when controlling for gender the correlation between height and weight drops to .770. Individual Height (inches) Weight (pounds) Sex (1 – male, 2 – female) A 73 240 1 B 70 210 1 C 69 180 1 D 68 160 1 E 70 150 2 F 68 140 2 G 67 135 2 H 62 120 2
  • 20. However, when controlling for gender the correlation between height and weight drops to .770. Individual Height (inches) Weight (pounds) Sex (1 – male, 2 – female) A 73 240 1 B 70 210 1 C 69 180 1 D 68 160 1 E 70 150 2 F 68 140 2 G 67 135 2 H 62 120 2 &
  • 21. However, when controlling for gender the correlation between height and weight drops to .770. Individual Height (inches) Weight (pounds) Sex (1 – male, 2 – female) A 73 240 1 B 70 210 1 C 69 180 1 D 68 160 1 E 70 150 2 F 68 140 2 G 67 135 2 H 62 120 2 &
  • 22. However, when controlling for gender the correlation between height and weight drops to .770. Individual Height (inches) Weight (pounds) Sex (1 – male, 2 – female) A 73 240 1 B 70 210 1 C 69 180 1 D 68 160 1 E 70 150 2 F 68 140 2 G 67 135 2 H 62 120 2 & controlling for
  • 23. However, when controlling for gender the correlation between height and weight drops to .770. Individual Height (inches) Weight (pounds) Sex (1 – male, 2 – female) A 73 240 1 B 70 210 1 C 69 180 1 D 68 160 1 E 70 150 2 F 68 140 2 G 67 135 2 H 62 120 2 & controlling for
  • 24. However, when controlling for gender the correlation between height and weight drops to .770. Individual Height (inches) Weight (pounds) Sex (1 – male, 2 – female) A 73 240 1 B 70 210 1 C 69 180 1 D 68 160 1 E 70 150 2 F 68 140 2 G 67 135 2 H 62 120 2 & controlling for = .770
  • 25. This is very helpful because we may think two variables (height and weight) are highly correlated but we can determine if that correlation holds when we take out the effect of a third variable (gender).
  • 26. While in partial correlation, only two variables are correlated while holding a third variable constant, in multiple regression several variables are grouped together to predict an outcome variable.
  • 27. While in partial correlation, only two variables are correlated while holding a third variable constant, in multiple regression several variables are grouped together to predict an outcome variable Independent or Predictor Variables
  • 28. While in partial correlation, only two variables are correlated while holding a third variable constant, in multiple regression several variables are grouped together to predict an outcome variable Independent or Predictor Variables Height
  • 29. While in partial correlation, only two variables are correlated while holding a third variable constant, in multiple regression several variables are grouped together to predict an outcome variable Independent or Predictor Variables Height Gender
  • 30. While in partial correlation, only two variables are correlated while holding a third variable constant, in multiple regression several variables are grouped together to predict an outcome variable Independent or Predictor Variables Height Gender Age
  • 31. While in partial correlation, only two variables are correlated while holding a third variable constant, in multiple regression several variables are grouped together to predict an outcome variable Independent or Predictor Variables Height Gender Age Soda Drinking
  • 32. While in partial correlation, only two variables are correlated while holding a third variable constant, in multiple regression several variables are grouped together to predict an outcome variable Independent or Predictor Variables Height Gender Age Soda Drinking Exercise
  • 33. While in partial correlation, only two variables are correlated while holding a third variable constant, in multiple regression several variables are grouped together to predict an outcome variable Independent or Predictor Variables Height Gender Age Soda Drinking Exercise Dependent, Response or Outcome Variable
  • 34. While in partial correlation, only two variables are correlated while holding a third variable constant, in multiple regression several variables are grouped together to predict an outcome variable Independent or Predictor Variables Height Gender Age Soda Drinking Exercise Dependent, Response or Outcome Variable Weight
  • 35. While in partial correlation, only two variables are correlated while holding a third variable constant, in multiple regression several variables are grouped together to predict an outcome variable Independent or Predictor Variables Height Gender Age Soda Drinking Exercise Dependent, Response or Outcome Variable Weight all have an influence on . . .
  • 36. While in partial correlation, only two variables are correlated while holding a third variable constant, in multiple regression several variables are grouped together to predict an outcome variable Independent or Predictor Variables Height Gender Age Soda Drinking Exercise Dependent, Response or Outcome Variable Weight all have an influence on . . .
  • 37. While in partial correlation, only two variables are correlated while holding a third variable constant, in multiple regression several variables are grouped together to predict an outcome variable Independent or Predictor Variables Height Gender Age Soda Drinking Exercise Dependent, Response or Outcome Variable Weight all have an influence on . . .
  • 38. While in partial correlation, only two variables are correlated while holding a third variable constant, in multiple regression several variables are grouped together to predict an outcome variable Independent or Predictor Variables Height Gender Age Soda Drinking Exercise Dependent, Response or Outcome Variable Weight all have an influence on . . .
  • 39. While in partial correlation, only two variables are correlated while holding a third variable constant, in multiple regression several variables are grouped together to predict an outcome variable Independent or Predictor Variables Height Gender Age Soda Drinking Exercise Dependent, Response or Outcome Variable Weight all have an influence on . . .
  • 40. While in partial correlation, only two variables are correlated while holding a third variable constant, in multiple regression several variables are grouped together to predict an outcome variable Independent or Predictor Variables Height Weight Gender Age Soda Drinking Exercise Dependent, Response or Outcome Variable all have an influence on . . .
  • 41. In this presentation we will cover the following aspects of Multiple Regression: - Connection to Partial Correlation and ANCOVA - Unique contribution of each variable - Contribution of all variables at the same time - Type of data multiple regression can handle - Types of relationships multiple regression describes
  • 42. Essentially, the group of predictors are all covariates to each other. Independent or Predictor Variables Height Weight Gender Age Soda Drinking Exercise Dependent, Response or Outcome Variable all have an influence on . . .
  • 43. Meaning, Independent or Predictor Variables Height Weight Gender Age Soda Drinking Exercise Dependent, Response or Outcome Variable all have an influence on . . .
  • 44. Meaning, for example, Independent or Predictor Variables Height Weight Gender Age Soda Drinking Exercise Dependent, Response or Outcome Variable all have an influence on . . .
  • 45. Meaning, for example, that it is possible to identify the unique prediction power of height on weight Independent or Predictor Variables Height Weight Gender Age Soda Drinking Exercise Dependent, Response or Outcome Variable all have an influence on . . .
  • 46. Meaning, for example, that it is possible to identify the unique prediction power of height on weight Independent or Predictor Variables Gender Age Soda Drinking Exercise Dependent, Response or Outcome Variable all have an influence Height on . . . Weight
  • 47. Meaning, for example, that it is possible to identify the unique prediction power of height on weight after you’ve taken out the influence of all of the other predictors. Independent or Predictor Variables Gender Age Soda Drinking Exercise Dependent, Response or Outcome Variable all have an influence Height on . . . Weight
  • 48. Meaning, for example, that it is possible to identify the unique prediction power of height on weight after you’ve taken out the influence of all of the other predictors. Independent or Predictor Variables Gender Age Soda Drinking Exercise Dependent, Response or Outcome Variable all have an influence Height on . . . Weight
  • 49. For example, Independent or Predictor Variables Height Weight Gender Age Soda Drinking Exercise Dependent, Response or Outcome Variable all have an influence on . . .
  • 50. For example, here is the correlation between Height and Weight without controlling for all of the other variables. Independent or Predictor Variables Gender Age Soda Drinking Exercise Dependent, Response or Outcome Variable all have an influence Height on . . . Weight
  • 51. For example, here is the correlation between Height and Weight without controlling for all of the other variables. Independent or Predictor Variables Gender Age Soda Drinking Exercise Dependent, Response or Outcome Variable all have an influence Height on . . . Weight Correlation = .825
  • 52. However, Independent or Predictor Variables Height Weight Gender Age Soda Drinking Exercise Dependent, Response or Outcome Variable all have an influence on . . .
  • 53. However, here is the correlation between Height and Weight after taking out the effect of all of the other variables. Independent or Predictor Variables Height Weight Gender Age Soda Drinking Exercise Dependent, Response or Outcome Variable all have an influence on . . .
  • 54. However, here is the correlation between Height and Weight after taking out the effect of all of the other variables. Independent or Predictor Variables Gender Age Soda Drinking Exercise Dependent, Response or Outcome Variable all have an influence on . . . Weight Height
  • 55. However, here is the correlation between Height and Weight after taking out the effect of all of the other variables. Independent or Predictor Variables Gender Age Soda Drinking Exercise Dependent, Response or Outcome Variable all have an influence Height on . . . Weight Correlation = .601
  • 56. However, here is the correlation between Height and Weight after taking out the effect of all of the other variables. Independent or Predictor Variables Gender Age Soda Drinking Exercise Dependent, Response or Outcome Variable all have an influence on . . . Weight Correlation = .601 So, after eliminating the effect of gender, age, soda, and exercise on weight, the unique correlation that height shares with weight is .601. Height
  • 57. Even though we were only correlating height and weight when we computed a correlation of .825,
  • 58. Even though we were only correlating height and weight when we computed a correlation of .825, the other four variables still had an influence on weight.
  • 59. Even though we were only correlating height and weight when we computed a correlation of .825, the other four variables still had an influence on weight. However, that influence was not accounted for and remained hidden.
  • 60. With multiple regression we can control for these four variables and account for their influence
  • 61. With multiple regression we can control for these four variables and account for their influence thus calculating the unique contribution height makes on weight without their influence being present.
  • 62. We can do the same for any of these other variables. Like the relationship between Gender and Weight.
  • 63. We can do the same for any of these other variables. Like the relationship between Gender and Weight. Independent or Predictor Variables Height Age Soda Drinking Exercise Dependent, Response or Outcome Variable all have an influence on . . . Weight Gender
  • 64. We can do the same for any of these other variables. Like the relationship between Gender and Weight. Independent or Predictor Variables Height Age Soda Drinking Exercise Dependent, Response or Outcome Variable all have an influence on . . . Weight Gender Correlation = .701
  • 65. But when you take out the influence of the other variables the correlation drops from .701 to .582.
  • 66. BEFORE Independent or Predictor Variables Height Age Soda Drinking Exercise Dependent, Response or Outcome Variable all have an influence on . . . Weight Gender Correlation = .701
  • 67. AFTER
  • 68. AFTER Independent or Predictor Variables Height Age Soda Drinking Exercise Dependent, Response or Outcome Variable all have an influence on . . . Weight Gender
  • 69. AFTER Independent or Predictor Variables Height Age Soda Drinking Exercise Dependent, Response or Outcome Variable all have an influence on . . . Weight Gender Correlation = .582
  • 70. Here is the correlation between age and weight before you take out the effect of the other variables:
  • 71. Here is the correlation between age and weight before you take out the effect of the other variables: Independent or Predictor Variables Height Gender Soda Drinking Exercise Dependent, Response or Outcome Variable all have an influence on . . . Age Weight
  • 72. Here is the correlation between age and weight before you take out the effect of the other variables: Independent or Predictor Variables Height Gender Soda Drinking Exercise Dependent, Response or Outcome Variable all have an influence on . . . Age Weight Correlation = .435
  • 73. The correlation drops from .435 to .385 after taking out the influence of the other variables:
  • 74. The correlation drops from .435 to .385 after taking out the influence of the other variables: Independent or Predictor Variables Height Gender Soda Drinking Exercise Dependent, Response or Outcome Variable all have an influence on . . . Age Weight
  • 75. The correlation drops from .435 to .385 after taking out the influence of the other variables: Independent or Predictor Variables Height Gender Soda Drinking Exercise Dependent, Response or Outcome Variable all have an influence on . . . Age Weight Correlation = .385
  • 76. In this presentation we will cover the following aspects of Multiple Regression: - Connection to Partial Correlation and ANCOVA - Unique contribution of each variable - Contribution of all variables at the same time - Type of data multiple regression can handle - Types of relationships multiple regression describes
  • 77. Beyond estimating the unique power of each predictor,
  • 78. Beyond estimating the unique power of each predictor, multiple regression also estimates the combined power of the group of predictors.
  • 79. Beyond estimating the unique power of each predictor, multiple regression also estimates the combined power of the group of predictors.
  • 80. Beyond estimating the unique power of each predictor, multiple regression also estimates the combined power of the group of predictors. Independent or Predictor Variables Height Weight Gender Age Soda Drinking Exercise Dependent, Response or Outcome Variable
  • 81. Beyond estimating the unique power of each predictor, multiple regression also estimates the combined power of the group of predictors. Independent or Predictor Variables Height Weight Gender Age Soda Drinking Exercise Dependent, Response or Outcome Variable Combined Correlation = .982
  • 82. In this presentation we will cover the following aspects of Multiple Regression: - Connection to Partial Correlation and ANCOVA - Unique contribution of each variable - Contribution of all variables at the same time - Type of data multiple regression can handle - Types of relationships multiple regression describes
  • 83. Multiple regression can estimate the effects of continuous and categorical variables in the same model.
  • 84. Multiple regression can estimate the effects of continuous and categorical variables in the same model. Independent or Predictor Variables Height Dependent, Response or Outcome Variable Gender Age Soda Drinking Exercise Weight
  • 85. Multiple regression can estimate the effects of continuous and categorical variables in the same model. Independent or Predictor Variables Height Height is represented by continuous data – because height can take on any value between two points in inches or centimeters. Dependent, Response or Outcome Variable Gender Age Soda Drinking Exercise Weight
  • 86. Multiple regression can estimate the effects of continuous and categorical variables in the same model.
  • 87. Multiple regression can estimate the effects of continuous and categorical variables in the same model. Independent or Predictor Variables Height Age Soda Drinking Exercise Dependent, Response or Outcome Variable all have an influence on . . . Weight Gender Gender is a represented by categorical data – because gender can take on two values (female or male)
  • 88. In this presentation we will cover the following aspects of Multiple Regression: - Connection to Partial Correlation and ANCOVA - Unique contribution of each variable - Contribution of all variables at the same time - Type of data multiple regression can handle - Types of relationships multiple regression describes
  • 89. Multiple regression can describe or estimate linear relationships like average monthly temperature and ice cream sales:
  • 90. Multiple regression can describe or estimate linear relationships like average monthly temperature and ice cream sales: 700 600 500 400 300 200 100 0 0 20 40 60 80 100 120 Ave Monthly Temperature Average Monthly Ice Cream Sales
  • 91. Multiple regression can describe or estimate linear relationships like average monthly temperature and ice cream sales: 700 600 500 400 300 200 100 0 0 20 40 60 80 100 120 Ave Monthly Temperature Average Monthly Ice Cream Sales
  • 92. It can also describe or estimate curvilinear relationships.
  • 94. For example, what if in our fantasy world the temperature reached 100 degrees and then 120 degrees. Let’s say with such extreme temperatures ice cream sales actually dip as consumers seek out products like electrolyte-enhanced drinks or slushies.
  • 95. Then the relationship might look like this:
  • 96. Then the relationship might look like this: 700 600 500 400 300 200 100 0 0 20 40 60 80 100 120 Ave Monthly Temperature Average Monthly Ice Cream Sales
  • 97. Then the relationship might look like this: 700 600 500 400 300 200 100 0 0 20 40 60 80 100 120 Ave Monthly Temperature Average Monthly Ice Cream Sales This is an example of a Curvilinear Relationship
  • 99. In summary, Multiple Regression is like single linear regression but instead of determining the predictive power of one variable (temperature) on another variable (ice cream sales) we consider the predictive power of other variables (such as socio-economic status or age).
  • 100. With multiple regression you can estimate the predictive power of many variables on a certain outcome,
  • 101. With multiple regression you can estimate the predictive power of many variables on a certain outcome, as well as the unique influence each single variable makes on that outcome after taking out the influence of all of the other variables.