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1 Suppose you the multiple regression model 60+ 63x1 62x2 + € ton O data points and obtain the following result: 9 3.4 4.6x1 2.7x2 -0-93x, The estimated standard errors B, and B, are 1.86 and 29, ,respectively. a. Test the nul hypothesis Ho 6, Dagainst the alternative hypothesis He 62 =0. Usea .05. Test the null hypothesis Ho 63=Dagainst the alternative hypothesis He 6, 0. Use a .05. The null hypothesis Ho: 62= Ois not rejected In contrast, the null hypothesis Ho: 6:= Ois rejected Explain how thiscanhappen even though B2 >B 2. Use SPSSt fita second order model the following data x 3 4 5 6 y 2.7 3.8 4.5 5.0 5.3 5.2 a. Find SSE ands². b Do data provide sufficient evidence to indicate that the second -or der term provides information for the prediction of y? [Hint: Test Ho: 62 =0]. c. State the least squares prediction equation 3. Running manufacturing operation efficiently requires knowledge of the time takes employees to manufacture the product otherwise the cost of making the product cannot br determined Estimates o production time are frequently obtained using time studies. The datair the table below carne from arecent time study of sampleo 15 employees performing particular task on an automobile assembly line Time Assemble, Months (minutes) Experience, x 10 24 15 11 15 11 17 19 11 20 13 17 18 16 16 a. Run the multiple linear regression model ir SPSS. State the least squares prediction equation b Test 6: the alternative He .01 Does the term tothe model? c. Your conclusion drop quadratic term from the model. Doso the 6xx+tothe data. d. Define Bain exercise. Find 90% confidence interval for in thereducedmodelof part c. 4. Suppose you fit the modely 60 61x1 62X2- 63X1X2 64x2+ datapoints and get SSE .46andR²= 87. a. Do the values SSE and 'suggest that the model provides good f tothe data? Explain. b. Is the model of any usei predicting /? Test the nul hypothesis that E(y)=60; that Ho:62=62=63=64=65=0 against the alternative hypothesis Ha: least one of the parameters 6, 62, 6sis nonzero Use 05. 5. company that services copy machines interested developing regression model that will assist in personnel planning tneeds amodel that describes the relationship between thetime spent on preventive maintenance service call to a customer, and two independent variables: the number of copy machines be serviced, X1, and the service person's experience preventive maintenance, X2. Hours of Number Months maintenance copy machines experience 1.0 12 17.0 10 14.0 6.0 10 1.8 11.5 10 10 9.3 6.0 6 12.2 10 18 a. Fit the modely 60 62% 62X; + € tothe data. b Investigate whether the model useful. Test .10 c. Find for the fitted model. Interpret your results d. Fit the model y €tothe data Find for themodel ir part d Explain why ou should not relv solel on comparison of the two R² values for drawing conclusions about which model smore useful for predicting g. Do the data provide sufficient evidence indicate that the interaction term X1X2 contributes information for the prediction ofy? Hint: Test Ha 6, 01 Which modeli: more usefu for predicting v? h. Can you be certain that the model you selected inpart best model use inpredicting maintenance time Explain.

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