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i 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 i x 7 6 5 1 5 4 7 3 4 2 8 5 2 5 7 1 4 5 i y 97 86 78 10 75 62 101 39 53 33 118 65 25 71 105 17 49 68 Summary calculation results are: 1152 i y = , 81 i x = , ( ) 2 16,504 i y y = , ( ) 2 74.5 i x x = , ( ) ( ) 1098 i i y y x x = . Use hand calculations for parts a)-g) a) Obtain the estimated (fitted) regression equation. [2 marks] b) Plot the estimated regression function and the data. Also plot the residuals vs. the explanatory variable ( x ). How well does the estimated regression equation fit the data? [4 marks] c) Interpret 0 ˆ β in your regression equation. Does 0 ˆ β provide any relevant information here? Explain. [4 marks] d) Obtain a 95% confidence interval for 1 ˆ β . [6 marks] e) Conduct a t-test to determine whether or not there is a linear association between x and y . State the alternative hypothesis, decision rule, and the conclusion. What is the p-value of your test? [4 marks] f) Obtain an approximate 95% prediction interval for the service time on the next service call in which six machines are serviced. Interpret your prediction interval. [6 marks]
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