A local tire dealer wants to predict the number of tires sold each month. The dealer believes that the number of tires sold is a linear function of the amount of money invested in advertising. The dealer randomly selects 6 months of data consisting of tire sales (in thousands of tires) and advertising expenditures (in thousands of dollars). Based on the data set with 6 observations, the simple linear regression model yielded the following results.
$$\sum x$$ = 24 $$\sum X ^ { 2 }$$ =124 $$\sum Y$$ =42 $$\sum Y ^ { 2 }$$ =338 $$\sum X Y$$ =196
-What is the value of regression sum of squares,or the explained variation?
A)24
B)28
C)44
D)16
E)6

Question

Quizplus · Accepted Answer

The regression sum of squares (explained variation) can be calculated using the formula: $$SSR = \frac{(\sum XY)^2}{\sum X^2} - \frac{(\sum X)^2}{n}$$ where $n$ is the number of observations. Plugging in the given values: $$SSR = \frac{(196)^2}{124} - \frac{(24)^2}{6} = \frac{38416}{124} - \frac{576}{6} = 310 - 96 = 214$$ However, there seems to be a mistake in my calculation as none of the provided options match the result. Let's correct the approach for calculating the regression sum of squares (SSR), which actually involves the coefficient of determination (R^2) or the slope and intercept of the regression line, neither of which are directly provided here. The correct approach to find SSR involves understanding the relationship between the total sum of squares (SST), the sum of squares of the residuals (SSE), and SSR itself, where SSR = SST - SSE. Without the direct means to calculate SSR from the provided sums and without the correct formula applied, the calculation above is incorrect. The correct approach would involve using the regression equation parameters (slope and intercept), which are not directly calculable with the provided information. Therefore, my initial calculation does not lead to a correct answer based on the options given, indicating a misunderstanding in the application of formulas for SSR in this context.

A Local Tire Dealer Wants to Predict the Number of Tires