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Q1. [5+10] Let us consider the Sales data. (a) Fit a normal linear regression model considering sales as a response variable. Is the fitted model significant at the 5% level of significant? Sales Change Accts WkLoad Time Adver 3669.88 0.34 74.86 15.05 43.10 4582.9 3473.95 0.15 107.32 19.97 108.13 5539.8 2295.10 -0.72 96.75 17.34 13.82 2950.4 4675.56 0.17 195.12 13.40 186.18 2243.1 6125.96 0.50 180.44 17.64 161.79 7747.1 2134.94 0.15 104.88 16.22 8.94 402.4 5031.66 0.55 256.10 18.80 365.04 3140.6 3367.45 -0.49 126.83 19.86 220.32 2086.2 6519.45 1.24 203.25 17.42 127.64 8846.3 4876.37 0.31 119.51 21.41 105.69 5673.1 2468.27 0.37 116.26 16.32 57.72 2761.8 2533.31 -0.65 142.28 14.51 23.58 1991.8 2408.11 0.64 89.43 19.35 13.82 1971.5 2337.38 1.01 84.55 20.02 13.82 1737.4 4586.95 0.11 119.51 15.26 86.99 10694.2 2729.24 0.04 80.49 15.87 165.85 8618.6 3289.40 0.68 136.58 7.81 116.260 7747.9 2800.78 0.66 78.86 16.00 42.280 4565.8 3264.20 -0.10 136.58 17.44 52.840 6022.7 3453.62 -0.03 138.21 17.98 165.040 3721.1 1741.45 -1.63 75.61 20.99 10.570 861.0 2035.75 -0.43 102.44 21.66 13.820 3571.5 1578.00 0.04 76.42 21.46 8.130 2845.5 4167.44 0.22 136.58 24.78 58.540 5060.1 2799.97 -0.74 88.62 24.96 21.140 3552.0 (b) Fit another regression model taking the last three explanatory variables. Do you think this new fit is significantly different from the fit given in (a)? Q2. [15] Three different machines produce a monofilament fiber for a textile company. The process engineer is interested in determining if there is a difference in breaking strength of the fiber produced by the three machines. However, the strength of a fiber is related to its diameter, with thicker fibers being generally stronger than thinner ones. A random sample of 5 specimens is selected from each machine. The fiber strength (y) and corresponding diameter (x) for each specimen is given below. Machine 1 Machine 2 Machine 3 y x y x y x 31 15 38 20 31 20 39 24 39 22 42 26 42 25 45 30 34 21 49 32 44 28 32 15 50 31 41 24 36 25 Fit an ANCOVA model to this data. Is the covariance has significant impact on this fit?

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