Question

PLEASE SHOW ALL EXCEL FORMULAS USED FOR EACH CALCULATIONS. A STEP BY STEP WALKTHROUGH OF HOW TO DO THE PROBLEM. Thank you so much for your help!

Hours   Feet   Elevator   Elevator code
24.00   545   Yes   1
13.50   400   Yes   1
26.25   562   No   0
25.00   540   No   0
9.00   220   Yes   1
20.00   344   Yes   1
22.00   569   Yes   1
11.25   340   Yes   1
50.00   900   Yes   1
12.00   285   Yes   1
38.75   865   Yes   1
40.00   831   Yes   1
19.50   344   Yes   1
18.00   360   Yes   1
28.00   750   Yes   1
27.00   650   Yes   1
21.00   415   No   0
15.00   275   Yes   1
25.00   557   Yes   1
45.00   1028   Yes   1
29.00   793   Yes   1
21.00   523   Yes   1
22.00   564   Yes   1
16.50   312   Yes   1
37.00   757   No   0
32.00   600   No   0
34.00   796   Yes   1
25.00   577   Yes   1
31.00   500   Yes   1
24.00   695   Yes   1
40.00   1054   Yes   1
27.00   486   Yes   1
18.00   442   Yes   1
62.50   1249   No   0
53.75   995   Yes   1
79.50   1397   No   0

USE THE ABOVE NUMBER AND ANSWER (A.) ACCORDING TO THE CHART

PARTS B AND BELOW ARE FROM THE EXAMPLE___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

The owner of a moving company wants an accurate method to predict the total number of labor hours that will be required to complete upcoming moves. The owner has decided to use the number of cubic feet moved and whether there is an elevator in the apartment building as the independent variables and has collected data for 36 moves. Use the data set given below to complete parts (a) through (g). For parts (a) through (d), do not include an interaction term EEB Click the icon to view the data table. a. State the multiple regression equation that predicts labor hours, when there is no elevator and define x2 to be 1 when there is an elevator. using the number of cubic fet moved, X1. and whether there is an elevator, X2. Define X2 to be o (Round to three decimal places as needed.) b. Interpret the regression coefficients in (a) To interpret the coefficient of a multiple regression model, hold constant all other coefficients in the model and then explain the effect of an increase of 1 in that coefficient. c. At the 0.05 level of significance, determine whether each independent variable makes a contribution to the regression model. Test the first independent variable, Feet. To test this variable, determine whether the slope, p1, of the variable Feet, Xj, is significantly different from 0. Determine the null and alternative hypotheses d. Construct and interpret a 95% confidence interval estimate of the population slope of the relationship between labor hours and number of cubic feet moved. Although either technology or the formula for confidence interval estimate of the slope could be used, for the purpose of this solution, use technology. Some technology will include the confidence interval estimates into the regression output, as shown below. Add the 95% confidence interval estimate for Feet into the output, rounding to three decimal places. Note that several values in the table have been left blank because they will be used in part (e). e. Construct and interpret a 95% confidence interval estimate of the population slope of the relationship between labor hours and whether there is an elevator. Use technology to add the 95% confidence interval estimate for Elevator into the output, rounding to three decimal places. Predictor Constant Feet Elevator Coef SE Coef 7.689 0.046 9.316 P 2.522 3.048 0.0045 0.003 14.437 0.0000 1.826 -5.101 0.0000 Lower 95% 2.557 0.039 13.032 Upper 95% 12.821 0.052 5.601 f. Add an interaction term to the model and, at the 0.05 level of significance, determine whether it makes a significant contribution to the model To find the multiple regression equation that predicts the selling price, based on the number of cubic feed moved, X1, whether there is an elevator, X2, and the interaction term, X3 -X1 XX2, first determine the values of the interaction term, X3 Multiply the values of the variable Feet by the corresponding values of the dummy variable Elevator (replacing "Yes" with 1 and "No" with 0) to determine the values of the interaction term. g. On the basis of the results of (c) and (f), which model is most appropriate? Explain. Review parts (c) and (f) carefully to determine which regression model is the most appropriate. Recall that the p-value for the test of H0: β1-0 versus H1 : β1 #0 (interaction term not included) was 0.0000, the p-value for the test of H0: β2-0 versus H1 : β2 #0 (interaction term not included) was 0.0000, and the p-value for the test of H0: ß3-0 versus H1 : ß3 #0 (interaction term included) was 0.0119.

Answer 1

a. Yi-2.451 + 0.048X!i-4.528Xp b. If we increase the number of cubic feet moved by 1 unit and if there is no elevator then the predicted la- bor hours is increased by 0.048 hrs. and if there is an el evator then the predicted labor hours is decreased by 4.48 hrs. C. Let B.-regression coefficient of X, of true regres- sion line Null hypothesis, Hol : βί 0 vs. Alternative hy- pothesis, Hi : B 0. For Ho1 the value of test statistic t 16.015 and corresponding p-value 4.00741 x 10-170.05 Hence we reject H01 at 5% level of significance and conclude that B is signiicantly different from zero. Similarly we reject H02 at 5% level of significance since since p-value corresponding X2 0.0388<

0.05 (see excel output) and conclude that B2 is sig- nificantly different from zero. Therefore both the variables X1 and X2 significantly con tribute to the regression model. (For detail, please see Excel output) d. 95% CI. for is (0.042, 0.054) e, 95% C.1. for B2 is (-8.809, -0.247) 1 IS

Hours(YFeet(X1 Elevator code(X2 SUMMARY OUTPUT 13 26.25 Regression Statistics MultipleR R Square Adjusted R Square Standard Error Observations 562 0.950198634 0.902877444 0.896991228 4.782486593 11.25 ANOVA Significance F MS 38.75 Regression Residual Total 2 7016.655626 3508.328 153.3884 33 754.7818744 22.87218 35 1-95336Е-17 831 19.5 7771.4375 Coefficients Standard Error tStat P-value Lower 95% Upper 95% Interce Feet(X1 Elevator code(X2 3.61879632 8.521238243 0.048 0.00300999 16.015 4.01E-17 0.042081103 0.054328843 -4.528 2.104084375-2.15214 0.038797 -8.809066192-0.247482498 2.451 2.983520099 0.821587 0.417209 415 10 45 793 523 16. 75 25 57 31 62.5 995 139 79.5