Calculate the coefficient of determination

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Reference no: EM132208261

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)

13 17.0

20 30.0

28 37.0

32 47.0

17 30.5

24 32.5

40 51.5

38 40.0

(a) Using a simple linear regression model with "Annual Maintenance Expense" being the dependent variable and "Weekly Usage" being the independent variable, EMBED Equation.3 , and following the Ordinary Least Squares method, find the OLS line: EMBED Equation.3 . 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 yi, i.e., EMBED Equation.3 , and all the residuals, i.e., ei. Show your work.

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

(e) Compute sy.x (=s?), the standard error of the model. Show your work.

(f) Find a 90% 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.

(i) Calculate the Simple Correlation Coefficient, r, and interpret its value. Show your work.

Reference no: EM132208261

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