Instruction 12.34
The management of a chain electronic store would like to develop a model for predicting the weekly sales (in thousands of dollars) for individual stores based on the number of customers who made purchases. A random sample of 12 stores yields the following results:
$$\begin{array} { | l | c | }
\hline \text { Customers } & \text { Sales (Thousands of Dollars) } \
\hline 907 & 11.20 \
\hline 926 & 11.05 \
\hline 713 & 8.21 \
\hline 741 & 9.21 \
\hline 780 & 9.42 \
\hline 898 & 10.08 \
\hline 510 & 6.73 \
\hline 529 & 7.02 \
\hline 460 & 6.12 \
\hline 872 & 9.52 \
\hline 650 & 7.53 \
\hline 603 & 7.25 \
\hline
\end{array}$$
-Referring to Instruction 12.34,the value of the F test statistic equals the square of the t test statistic when testing whether the number of customers who make purchases is a good predictor for weekly sales.

Question

Instruction 12.34
The management of a chain electronic store would like to develop a model for predicting the weekly sales (in thousands of dollars) for individual stores based on the number of customers who made purchases. A random sample of 12 stores yields the following results:
 $$\begin{array} { | l | c | } 
\hline \text { Customers } & \text { Sales (Thousands of Dollars) } \
\hline 907 & 11.20 \
\hline 926 & 11.05 \
\hline 713 & 8.21 \
\hline 741 & 9.21 \
\hline 780 & 9.42 \
\hline 898 & 10.08 \
\hline 510 & 6.73 \
\hline 529 & 7.02 \
\hline 460 & 6.12 \
\hline 872 & 9.52 \
\hline 650 & 7.53 \
\hline 603 & 7.25 \
\hline
\end{array}$$
-Referring to Instruction 12.34,the value of the F test statistic equals the square of the t test statistic when testing whether the number of customers who make purchases is a good predictor for weekly sales.

Quizplus · Accepted Answer

This statement is true. When performing simple linear regression, the F test statistic is equal to the square of the t test statistic for the regression coefficient. In this case, the regression coefficient represents the relationship between the number of customers and weekly sales. Therefore, the F test can be used to test the overall significance of the relationship between these two variables, and the F statistic will be the square of the t statistic for the regression coefficient.

Instruction 12 -Referring to Instruction 12