Linear regression
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Linear regression analyzes the relationship between two variables, where one variable (X) is considered to predict or cause changes in the other variable (Y). It fits a straight line through the data points on a scatterplot to represent the trend of Y values as X changes. The regression line shows the average relationship between X and Y, allowing Y values to be estimated based on X. Higher correlation values (closer to 1 or -1) indicate stronger linear relationships between the variables.
Linear regression
- 2. Linear Regression Involves two variables that are paired because there is a relationship between them Deal with measurements made on two variables X and Y - bivariate Ex. height and weight, achievement & learning approach, study habits & grades, achievement and aptitude
- 3. Linear Regression There is a straight line relationship between variables X and Y When X increases, Y also increases- positive relationship When X increases, Y decreases or vice versa – negative relationship
- 4. Relationship between achievement and aptitude Achievement (X) Aptitude (Y) 100 99 95 98 90 94 85 87 82 84 80 81 75 78 70 73 65 68 50 60
- 5. Regression Line between achievement and aptitude Scatterplot: X v s. Y Y = 14.379 + .85633 * X Correlation: r = .98966 105 100 95 90 85 80 Y 75 70 65 60 55 40 50 60 70 80 90 100 110 X 95% conf idence
- 6. Laziness Perseverance 100 35 95 40 90 45 85 50 75 55 70 60 65 64 60 70 55 76 50 80
- 7. Relationship between Laziness and Perseverance Scatterplot: Y v s. X X = 139.94 - 1.138 * Y Correlation: r = -.9959 110 100 90 80 X 70 60 50 40 30 40 50 60 70 80 90 Y 95% conf idence
- 8. Y can be predicted based on the value of X Y = a + bX