The owner of a moving company has collected data to predict how many labor hours

Question

The owner of a moving company has collected data to predict how many labor hours a move will take based on the number of cubic feet moved. The data below has been collected from 20 moves. The results are displayed in the accompanying table, and the regression equation and other values are shown below. Use this information to complete parts (s) through (c) below. Y_1 = - 4.0277 + 0.0590 X_i sigma^n _i = 1 Y_1 = 577.25, sigma^n _i = 1 Y^2 _i = 18, 152.5625, sigma^n _i = 1 X_i Y_i = 341, 7385 a. Determine the coefficient of determination, r^2, and interpret its meaning r^2 = (Round to four decimal places as needed.) What is the meaning of the coefficient of determination? A. It measures the variability in the number of cubic feet moved from the predicted number of cubic feet moved. B. It measures the variability in the actual labor hours from the predicted labor hours. C. It is the proportion of the variation in the number of cubic feet moved that is explained by the variability in labor hours. D. It is the proportion of the variation in labor hours that is explained by the variability in the number of cubic feet moved. b. Determine the standard error of the estimate. S_yX - (Round to four decimal places as needed.) c. How useful do you think this regression model is for predicting the labor hours required for a move? Since the value of r^2 is the regression model is for predicting the labor hours required for a move.

Explanation / Answer

(a) r^2 = 0.7617 and option D

(b) 68.2210

(c) High, significant

Regression Analysis r² 0.762 n   20 r   0.873 k   1 Std. Error   68.221 Dep. Var. y ANOVA table Source SS   df   MS F p-value Regression 267,774.9435 1   267,774.9435 57.54 5.19E-07 Residual 83,774.0065 18   4,654.1115 Total 351,548.9500 19   Regression output confidence interval variables coefficients std. error    t (df=18) p-value 95% lower 95% upper std. coeff. Intercept 168.3444 0.000 x 13.3982 1.7664 7.585 5.19E-07 9.6872 17.1092 0.873

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