Question

(Solve this problem manually.) Jensen Tire & Auto is in the process of deciding whether to purchase a maintenance contract for its new computer wheel alignment and balancing machine. Managers feel that maintenance expense should be related to usage, and they collected the following information on weekly usage (hours) and annual maintenance expense (in hundreds of dollars):

            Weekly Usage (hours)                       Annual Maintenance Expense ($100)

                        17                                                        17

                        20                                                        30

                        28                                                        40

                        32                                                        38

                        18                                                        31

                        24                                                        32.5

                        42                                                        41

                        35                                                        45

(a)        Using a simple linear regression model with “Annual Maintenance Expense”

            being the dependent variable and “Weekly Usage” being the independent

            variable, , and following the Ordinary Least Squares method, find the OLS line: . Show all your work.

(b)       Explain intuitively the slope estimate, b₁, in the context of the problem.

(c)        Using the OLS line as you derived in part (a), manually calculate all the predicted       values of y_i, i.e.,, and all the residuals, i.e., e_i. Show your work.

(d)       Compute SSE (Sum of Squared Errors). Show your work.

(e)        Compute s_y.x (=s_ɛ), the standard error of the model. Show your work.

(f)        Find a 99% confidence interval for β₁ and interpret the interval.

(g)       Test to see if “Weekly Usage” affects “Annual Maintenance Expense,” and if so,    in what direction? Use α = 0.05 and interpret your results.

(h)       Calculate the Coefficient of Determination, r². Based upon your calculation, do    you believe your model is a good model? Show your work and explain.

Answer 1

AAs per HOMEWORKLIB RULES we should solve only the first four sub parts of the question. Please post the other parts differently mentioning your requirements