The Owner of a Bakery Wants to Analyze the Relationship $\begin{array}{cc}Y&X\\\text { Expenditure }&\text { Income In Thousands }\\45 & 20 \\10.75 & 19 \\5.40 & 22 \\7.80 & 25 \\5.60 & 14\end{array}$

Essay

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.