Question: A local tire dealer wants to predict the number of tires sold each month. He believes that the number of tires sold is a linear function of the amount of money invested in advertising. He 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:

a) Determine the values of \({{b}_{0}}\) and \({{b}_{1}}\) in the simple linear regression equation of the least squares line: \(\hat{y}={{b}_{0}}+{{b}_{1}}x\). Show all your work. (20 Points)

b) Test \({{H}_{0}}:{{\beta }_{1}}\le 0\) vs. \({{H}_{A}}:{{\beta }_{1}}>0\) at a = 0.05 .