Correlation and regression
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Correlation and regression are statistical methods used to measure relationships between variables. Correlation determines how strongly two variables are related, yielding a correlation coefficient between -1 and 1. Positive correlation means variables increase together, while negative correlation means one variable decreases as the other increases. Regression finds the best-fit line for predicting a dependent variable from an independent variable. It determines whether knowing one variable provides information to predict another variable. The line of best fit minimizes the sum of squared errors between the observed data points and the fitted line.
Correlation and regression
- 2. Correlation • When two sets of data are strongly linked together we say they have a High Correlation. • The word Correlation is made of Co- (meaning "together"), and Relation • Correlation is Positive when the values increase together • Correlation is Negative when one value decreases as the other increases
- 3. Correlation • The local ice cream shop keeps track of how much ice cream they sell versus the temperature on that day
- 4. Correlation
- 6. Calculation of correlation Correlation coefficients are used to measure how strong a relationship is between two variables. There are several types of correlation coefficient, but the most popular is Pearson’s. Pearson’s correlation (also called linear correlation) is a correlation coefficient commonly used in linear regression Pearson Correlation Coefficient Formula: Correlation coefficient formulas are used to find how strong a relationship is between data. The formulas return a value between -1 and 1, where: 1 indicates a strong positive relationship. -1 indicates a strong negative relationship. A result of zero indicates no relationship at all
- 7. Calculation of correlation Correlation coefficients are used to measure how strong a relationship is between two variables. There are several types of correlation coefficient, but the most popular is Pearson’s. Pearson’s correlation (also called linear correlation) is a correlation coefficient commonly used in linear regression Pearson Correlation Coefficient Formula: Correlation coefficient formulas are used to find how strong a relationship is between data. The formulas return a value between -1 and 1, where: 1 indicates a strong positive relationship. -1 indicates a strong negative relationship. A result of zero indicates no relationship at all
- 9. Calculate the linear correlation coefficient for the following data. X = 4, 8 ,12, 16 and Y = 5, 10, 15, 20.
- 10. Given variables are, X = 4, 8 ,12, 16 and Y = 5, 10, 15, 20 For finding the linear coefficient of these data, we need to first construct a table for the required values.
- 11. Scatter Plots of Data with Various Correlation Coefficients Y X Y X Y X Y X Y X r = -1 r = -.6 r = 0 r = +.3 r = +1 Y X r = 0
- 12. Y X Y X Y Y X X Linear relationships Curvilinear relationships Linear Correlation
- 13. Y X Y X Y Y X X Strong relationships Weak relationships Linear Correlation
- 15. Linear regression In correlation, the two variables are treated as equals. In regression, one variable is considered independent (=predictor) variable (X) and the other the dependent (=outcome) variable Y. If you know something about X, this knowledge helps you predict something about Y.
- 16. Line of Best Fit Imagine you have some points, and want to have a line that best fits them like this: We can place the line "by eye": try to have the line as close as possible to all points, and a similar number of points above and below the line. But for better accuracy let's see how to calculate the line using Least Squares Regression.
- 17. Principle of least squares The method works by making the total of the square of the errors as small as possible (that is why it is called "least squares"): The straight line minimizes the sum of squared errors So, when we square each of those errors and add them all up, the total is as small as possible. It is often required to find a relationship between two or more variables. Least Square is the method for finding the best fit of a set of data points. It minimizes the sum of the residuals of points from the plotted curve.
- 18. Difference Between Correlation and Regression