12. Regression
Coefficient of Determination
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A retail analyst is studying the relationship between the number of in-store promotional displays (x) and weekly sales revenue (y) at 12 store locations. Use the data below and a calculator to find the coefficient of determination.
A
0.0031
B
0.0016
C
0.9984
D
0.9969
Verified step by step guidance1
Step 1: Understand the coefficient of determination (R²). It measures the proportion of the variance in the dependent variable (y, weekly revenue) that is predictable from the independent variable (x, number of displays). R² is calculated using the formula:
Step 2: Calculate the mean of x (number of displays) and y (weekly revenue). Use the formula for the mean:
Step 3: Compute the total sum of squares (SS_total) for y. Use the formula:
Step 4: Fit a linear regression model to the data to find the predicted values of y (ŷ). Use the formula for the regression line: where is the slope and is the intercept.
Step 5: Calculate the residual sum of squares (SS_residual) using the formula: Finally, substitute SS_residual and SS_total into the formula for R² to compute the coefficient of determination.
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