Consider the Supervisor Performance Data in Table 3.3 on page 60 of the TEXT .

1) Estimate the regression coefficients vector .

2) Verify that Pn i=1 yi = Pn i=1 yi for this dataset.

3) Does Pn i=1 yi = Pn i=1 yi hold true in general for multiple linear regression model Y = 0 + 1X1 + 2X2 + . . . + pXp + ? Prove or disprove it.

4) Now consider p = 2, and only use X3 and X4 two predictors. The model becomes Y = 0 + 3X3 + 4X4 + Use the 3-step method described on page 63 to obtain the coefficient for X3, and compare it with the coefficient of X3 by regressing Y on X3 and X4 using the 2-predictor model above. Are they the same? Explain why or why not.

Y X1 X2 X3 X4 X5 X6 43 51 30 39 61 92 45 63 64 51 54 63 73 47 71 70 68 69 76 86 48 61 63 45 47 54 84 35 81 78 56 66 71 83 47 43 55 49 44 54 49 34 58 67 42 56 66 68 35 71 75 50 55 70 66 41 72 82 72 67 71 83 31 67 61 45 47 62 80 41 64 53 53 58 58 67 34 67 60 47 39 59 74 41 69 62 57 42 55 63 25 68 83 83 45 59 77 35 77 77 54 72 79 77 46 81 90 50 72 60 54 36 74 85 64 69 79 79 63 65 60 65 75 55 80 60 65 70 46 57 75 85 46 50 58 68 54 64 78 52 50 40 33 34 43 64 33 64 61 52 62 66 80 41 53 66 52 50 63 80 37 40 37 42 58 50 57 49 63 54 42 48 66 75 33 66 77 66 63 88 76 72 78 75 58 74 80 78 49 48 57 44 45 51 83 38 85 85 71 71 77 74 55 82 82 39 59 64 78 39