The owner of a bakery wants to analyze the relationship between the expenditure of a customer and the customer's income. A sample of 5 customers is taken and the following information was obtained.
$\begin{array}{cc}Y&X\\text { Expenditure }&\text { Income In Thousands }\
45 & 20 \
10.75 & 19 \
5.40 & 22 \
7.80 & 25 \
5.60 & 14
\end{array}$ The least squares estimated line is $\hat { \mathrm { Y } }$ = 4.348 + 0.0826 X.
a. Obtain a measure of how well the estimated regression line fits the data.
b. You want to test to see if there is a significant relationship between expenditure and income at the 5% level of significance. Be sure to state the null and alternative hypotheses.
c. Construct a 95% confidence interval estimate for the average expenditure for all customers with an income of $20,000.
d. Construct a 95% confidence interval estimate for the expenditure of one customer whose income is $20,000.

Question

The owner of a bakery wants to analyze the relationship between the expenditure of a customer and the customer's income. A sample of 5 customers is taken and the following information was obtained.
 $\begin{array}{cc}Y&X\\text { Expenditure }&\text { Income In Thousands }\
45 & 20 \
10.75 & 19 \
5.40 & 22 \
7.80 & 25 \
5.60 & 14
\end{array}$ The least squares estimated line is $\hat { \mathrm { Y } }$ = 4.348 + 0.0826 X. 
a. Obtain a measure of how well the estimated regression line fits the data.
b. You want to test to see if there is a significant relationship between expenditure and income at the 5% level of significance. Be sure to state the null and alternative hypotheses.
c. Construct a 95% confidence interval estimate for the average expenditure for all customers with an income of $20,000.
d. Construct a 95% confidence interval estimate for the expenditure of one customer whose income is $20,000.

Quizplus · Accepted Answer

The Answer of The owner of a bakery wants to analyze the relationship between the expenditure of a customer and the customer's income. A sample of 5 customers is taken and the following information was obtained.
 $\begin{array}{cc}Y&X\\text { Expenditure }&\text { Income In Thousands }\
45 & 20 \
10.75 & 19 \
5.40 & 22 \
7.80 & 25 \
5.60 & 14
\end{array}$ The least squares estimated line is $\hat { \mathrm { Y } }$ = 4.348 + 0.0826 X. 
a. Obtain a measure of how well the estimated regression line fits the data.
b. You want to test to see if there is a significant relationship between expenditure and income at the 5% level of significance. Be sure to state the null and alternative hypotheses.
c. Construct a 95% confidence interval estimate for the average expenditure for all customers with an income of $20,000.
d. Construct a 95% confidence interval estimate for the expenditure of one customer whose income is $20,000.