Customer Oil Usage Degree Days Home Index Number People 1 381 888 3 3 2 171 176

Question

Customer Oil Usage Degree Days Home Index Number People 1 381 888 3 3 2 171 176 5 7 3 644 1073 5 4 4 19 126 2 4 5 394 645 5 5 6 153 326 4 6 7 7 1229 1 3 8 319 1218 2 4 9 40 570 2 1 10 121 334 1 7 11 243 738 3 3 12 200 1464 1 5 13 402 880 4 5 14 118 1134 1 5 15 319 1019 3 4 16 185 460 2 3 17 209 257 5 4 18 467 779 5 4 19 50 128 2 4 20 153 371 2 5 21 94 178 3 6 22 574 933 5 3 23 191 295 3 5 24 679 1358 4 5 25 305 626 4 5 26 85 237 2 7 27 87 813 1 6 28 170 385 3 5 29 92 678 1 4 30 35 54 2 3 31 60 314 1 5 32 507 898 4 3 33 148 966 1 6 34 83 84 5 3 35 318 919 3 4 36 85 379 1 4 37 245 512 3 4 38 56 355 2 3 39 303 759 3 3 40 10 777 1 4 QUESTION 7 7] The Y-intercept of the multiple regression model is significantly different from 0 in the population. O Yes No QUESTION 8 [8] The predicted Oil Usage of a customer for whom Degree Days equal 600, Home Index value is 3, and number of people living in the house is 4, is approximately 365 229 180 665 QUESTION 9 [9] The predicted Oil Usage of a customer for whom Degree Days equal 458, Home Index value is 1, and number of people living in the house is 1, is approximately: O 242 QUESTION 10 [10] The multiple regression model suggests that about 78% of the variation in the predictors can be explained by Oil Usage True False

Explanation / Answer

Here first we will evaluate a multiregression model and the regression analysis.

QUestion 7

For intercept

the value of intercept = -218.31

standard error = 63.9585

p - value = 0.0016 < 0.05

so yes the value of intercept is significant different from 0.

Question 8

Here Degree days = 600

Home Index = 3

Number of people living in the house = 4

here the regression model is

y^ = -218.31 + 0.2751 * Degree days + 86.9888 * Home index + 5.2672 * Number of people

y^ = -218.31 + 0.2751 * 600 + 86.9888 * 3 + 5.2672 * 4 = 228.7852 or 229

Question 9

Here Degree days = 458

Home Index = 1

Number of people living in the house = 1

here the regression model is

y^ = -218.31 + 0.2751 * Degree days + 86.9888 * Home index + 5.2672 * Number of people

y^ = -218.31 + 0.2751 * 458 + 86.9888 * 1 + 5.2672 * 1 = - 0.0582 or 0

Question

HEre R2 = 0.78

so the given statement is true.

SUMMARY OUTPUT Regression Statistics Multiple R 0.885464 R Square 0.784046 Adjusted R Square 0.76605 Standard Error 85.4675 Observations 40 ANOVA df SS MS F Significance F Regression 3 954738.9 318246.3 43.56737 4.55E-12 Residual 36 262969 7304.694 Total 39 1217708 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -218.31 63.95851 -3.4133 0.001602 -348.024 -88.596 -348.024 -88.596 Degree Days 0.275079 0.036333 7.571119 5.94E-09 0.201393 0.348765 0.201393 0.348765 Home Index 86.98875 9.630435 9.032692 8.75E-11 67.45732 106.5202 67.45732 106.5202 Number People 5.26724 10.56179 0.498707 0.62102 -16.1531 26.68755 -16.1531 26.68755

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