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 sales revenue) that is predictable from the independent variable (x, number of promotional displays). R² values range from 0 to 1, where values closer to 1 indicate a stronger relationship.
Step 2: Calculate the correlation coefficient (r) using the formula: r = (nΣ(xy) - ΣxΣy) / sqrt([(nΣx² - (Σx)²) * (nΣy² - (Σy)²)]). Here, n is the number of data points, Σx and Σy are the sums of x and y values, Σ(xy) is the sum of the product of x and y, Σx² is the sum of squared x values, and Σy² is the sum of squared y values.
Step 3: Once the correlation coefficient (r) is calculated, square it to find the coefficient of determination (R²). The formula is R² = r².
Step 4: Interpret the R² value. For example, if R² = 0.9969, it means that 99.69% of the variation in weekly sales revenue is explained by the number of promotional displays.
Step 5: Use a calculator or statistical software to perform the calculations efficiently, ensuring all sums and operations are accurate. Input the data from the table into the formulas provided in Step 2.
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