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APPENDIX TABLE LINK : https://www.webassign.net/mendstat15/mendstat15_appendix_tables.pdf

Q13.7

[-/2 Points] MendStat15 13.R.004. The effect of mean monthly daily temperature xi and cost per kilowatthour x2 on the mean daily household consumption of electricity (in kilowatt-hours, kWh) was the subject of a short-term study. The investigators expected the demand for electricity to rise in cold weather (due to heating), fall when the weather was moderate, and rise again when the temperature rose and there was need for air-conditioning. They expected demand to decrease as the cost per kilowatt- hour increased, reflecting greater attention to conservation. Data were available for 2 years, a period in which the cost per kilowatt-hour x2 increased because of the increasing cost of fuel. The company fitted the model E()) = Bo + PIXI + B2x12 + B3x2 + B4x1x2+ BSx12x2 to the data shown in the table. The Excel printout for this multiple regression problem is also provided Price per Daily Temperature Mean Daily Consumption kWh, x2 and Consumption (k Wh) per Household Mean daily 30 35 39 42 47 56 temperature ( F), x1 62 66 68 71 76 78 Mean daily 56 49 46 47 40 43 consumption, y 41 46 44 51 62 73 Mean daily 32 36 39 42 48 56 temperature, x1 62 66 68 72 75 79 10c Mean daily 50 44 42 42 38 40 consumption, y 39 44 40 44 50 55 SUMMARY OUTPUT Regression Statistics Multiple R 0.949 R Square 0.901 Adjusted R Square 0.874 Standard Error 2.887 Observations 24 ANOVA df SS MS Significance F Regression 5 1365.810 273.162 32.774 0.000 Residual 18 150.023 8.335 Total 23 1515.833 Coefficients Standard Error t Stat P Value Intercept 315.429 80.699 3.909 0.001 XI -10.892 3.142 -3.467 0.003 x1-sq 0.108 0.029 3.794 0.001 x2 -20.681 8.999 2.298 0.034x1x2 0.824 0.350 2.356 0.030 xIsqx2 -0.008 0.003 -2.631 0.017 (a) Do the data provide sufficient evidence to indicate that the model contributes information for the prediction of mean daily kilowatt-hour consumption per household? Test at the 5% level of significance. State the null and alternative hypotheses. C Ho: BI B2 > B3 > B4> Bs > O Ho: B1 = B2 = B3 = B4 = Bs Ha: At least one of B1, B2, B3, B4, Bs is different from the others. Ho: B1 = B2 = B3 = B4 = B5 = 0 Ha: At least one of B1, B2, B3, B4, Bs is not O. " Ho: Bi > B2 > B3 > B4 > Bs > O Ha: B1 = B2 = B3 = B4 = Bs =0 Find the test statistic. (Round your answer to three decimal places.) F =1 Approximate the p-value for the test. p-value 0.00 State your conclusion. C Ho is rejected. There is insufficient evidence to indicate that the model contributes information for the prediction of y. Ho is not rejected. There is insufficient evidence to indicate that the model contributes information for the prediction of y. Ho is not rejected. There is sufficient evidence to indicate that the model contributes information for the prediction of y. Ho is rejected. There is sufficient evidence to indicate that the model contributes information for the prediction of y. (b) Graph the curve depicting y as a function of temperature x1 when the cost per kilowatt-hour is X2 = 84. Construct a similar graph for the case when x2 = 10 per kilowatt-hour. Are the consumption curves different? Yes, they are different. No, they are not different. (c) If cost per kilowatt-hour is unimportant in predicting use, then you do not need the terms involving x2 in the model. Therefore, the null hypothesis Ho: X2 does not contribute information for the prediction of y is equivalent to the null hypothesis\fX2 = 0 X2 = 1 E(y) HOHNWAUG X2 = 2 1 N X1 (b What relationship do the lines in part (a) have to one another? The lines are all vertical. The lines are parallel. The lines intersect each other at the same point. The lines are all horizontal. 10. [-/2 Points] MendStat15 13.R.502.XP. Suppose that is related to two predictor variables, X1 and X2, by the equation E(y) = 6 + x1 -4x2. (a) Graph the relationship between and x2 when x1 = 0. Repeat for x1 = 1 and for x1 = 2.\f45'" 1'2 (b) What relationship do the lines in part (a) have to one another? I" The lines intersect each other at the same point. t" The lines are all horizontal. r The lines are all vertical. t" The lines are parallel. (C) Suppose, in a practical situation, you want to model the relationship between EU) and two predictor variables x1 and x2. What is the implication of using the rst-order model E(y) =30 +31)\" + 32362? f. The rst-order model E(y) = n + 31x1 + 15' 212 will be a twisted surface in three-dimensional Space. rt The rst-order model E(y) = [90 + 3m + zxz will be a plane in three-dimensional space. If" The rst-order model E(y) = e + 31x1 + [32x2 will be a straight line in two-dimensional space. If. The rst-order model E0!) = e + B 1x1 + zxz will be a set of intersecting lines in two- dimensional space