MULTIPLE LINEAR REGRESSION MODEL in .NET

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12-1 MULTIPLE LINEAR REGRESSION MODEL
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Table 12-7 TEMP 1650 1650 1650 1650 1600 1600 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1700 1650 1650 1700 1700 SOAKTIME 0.58 0.66 0.66 0.66 0.66 0.66 1.00 1.17 1.17 1.17 1.17 1.17 1.17 1.20 2.00 2.00 2.20 2.20 2.20 2.20 2.20 2.20 3.00 3.00 3.00 3.00 3.33 4.00 4.00 4.00 12.50 18.50 SOAKPCT 1.10 1.10 1.10 1.10 1.15 1.15 1.10 1.10 1.10 1.10 1.10 1.10 1.15 1.15 1.15 1.10 1.10 1.10 1.15 1.10 1.10 1.10 1.15 1.10 1.10 1.15 1.10 1.10 1.10 1.15 1.00 1.00 DIFFTIME 0.25 0.33 0.33 0.33 0.33 0.33 0.50 0.58 0.58 0.58 0.58 0.58 0.58 1.10 1.00 1.10 1.10 1.10 1.10 1.10 1.10 1.50 1.50 1.50 1.50 1.66 1.50 1.50 1.50 1.50 1.50 1.50 DIFFPCT 0.90 0.90 0.90 0.95 1.00 1.00 0.80 0.80 0.80 0.80 0.90 0.90 0.90 0.80 0.80 0.80 0.80 0.80 0.80 0.90 0.90 0.90 0.80 0.70 0.75 0.85 0.80 0.70 0.70 0.85 0.70 0.70 PITCH 0.013 0.016 0.015 0.016 0.015 0.016 0.014 0.021 0.018 0.019 0.021 0.019 0.021 0.025 0.025 0.026 0.024 0.025 0.024 0.025 0.027 0.026 0.029 0.030 0.028 0.032 0.033 0.039 0.040 0.035 0.056 0.068
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(SOAKPCT, SOAKTIME), and carbon concentration and duration of the diffuse cycle (DIFFPCT, DIFFTIME). (a) Fit a linear regression model relating the results of the pitch carbon analysis test (PITCH) to the five regressor variables. (b) Estimate 2. (c) Find the standard errors se 1 j 2. (d) Use the model in part (a) to predict PITCH when TEMP 1650, SOAKTIME 1.00, SOAKPCT 1.10, DIFFTIME 1.00, and DIFFPCT 0.80. 12-11. Statistics for 21 National Hockey League teams were obtained from the Hockey Encyclopedia and are shown in Table 12-8.
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The variables and definitions are as follows: Wins Number of games won in a season. Pts Points awarded in a season. Two points for winning a game, one point for losing in overtime, zero points for losing in regular time. GF Goals for. Total goals scored during the season. GA Goals against. Goals scored against the team during the season. PPG Power play goals. Points scored while on power play. PPcT Power play percentage. The number of power play goals divided by the number of power play opportunities.
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Table 12-8 Team
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CHAPTER 12 MULTIPLE LINEAR REGRESSION
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Wins 47 40 28 25 21 47 32 30 33 27 49 42 39 35 17 18 50 42 38 34 19
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Pts 104 96 68 65 57 106 78 75 74 66 106 96 94 80 48 45 110 98 89 80 45
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GF 338 321 23 285 263 424 321 303 311 308 326 302 306 306 230 257 327 350 318 343 261
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GA 268 290 330 316 344 315 317 309 333 365 240 226 283 287 338 394 228 286 285 336 403
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PPG 86 91 79 67 37 86 90 65 78 81 60 69 75 71 66 81 67 64 67 61 51
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PPcT 27.2 26.4 22.3 21.2 19.3 29.3 27 23.8 23.6 23.8 21.6 25.8 20.9 22.4 21.9 22.6 22.2 22.2 21.5 20.7 19.3
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SHG 4 17 13 9 7 22 7 5 10 10 15 10 3 12 74 3 8 8 12 6 6
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PPGA 71 67 83 63 80 89 59 56 67 94 61 55 53 75 78 110 53 68 48 92 70
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PKPcT 76.6 80.7 75 81.3 72.6 77.5 77.1 80.8 72.8 68.2 82 83.4 81.6 76 73.5 72.2 80.7 73.8 82.5 73.6 76.1
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SHGA 6 20 9 12 9 6 6 13 7 14 7 3 11 8 10 15 6 8 9 6 9
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Chicago Minnesota Toronto St. Louis Detroit Edmonton Calgary Vancouver Winnipeg Los Angeles Philadelphia NY Islanders Washington NY Rangers New Jersey Pittsburgh Boston Montreal Buffalo Quebec Hartford
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Short-handed goals scored during the season. Power play goals against. Penalty killing percentage. Measures a team s ability to prevent goals while its opponent is on a power play. Opponent power play goals divided by opponent s opportunities. Short-handed goals against. Fit a multiple linear regression model relating wins to the other variables. Estimate 2 and find the standard errors of the regression coefficients.
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12-12.
Consider the linear regression model Yi 0
1 1xi1
where x1 g xi1 n and x2 g xi2 n. (a) Write out the least squares normal equations for this model. (b) Verify that the least squares estimate of the intercept in this model is g yi n y. 0 (c) Suppose that we use yi y as the response variable in the model above. What effect will this have on the least squares estimate of the intercept
x1 2
2 1xi2
x2 2
12-2
HYPOTHESIS TESTS IN MULTIPLE LINEAR REGRESSION
In multiple linear regression problems, certain tests of hypotheses about the model parameters are useful in measuring model adequacy. In this section, we describe several important hypothesis-testing procedures. As in the simple linear regression case, hypothesis testing requires that the error terms i in the regression model are normally and independently distributed with mean zero and variance 2.
12-2.1