Question

The owner of a TIoving company typically has his riost experienced manager predict the total number of labor hours that will be required to complete an upcoming move. In an effort to provide a more accurate method, the owner has Use the data provided to complete parts (a) which the travel tirme was aı insignificant portion of the hours worker number of cubic feet moved as the independent variable and has collected data for 20 moves through (d) below EClick the Icon to vlew the data table. a. Construct a scatter plot. Choose the correct graph below. O C. O B. O D. 9004 co- 0- 00- Cubic Feet Cubic Fee Hours Hours b. Assuming a linear relationship, use the least-squares method to determine the reqression coefficients b, and b.- b b, Round to three decimal places as needed.) c. Interpret the meaning of the slope, b, in this problem. Chouse the correct answer below. A, The approximate number of cubic feet moved when the number f labor hours is 0 hours is b. B. For each increase of one cubic foot moved, the number of labor hours is expected to increase by b, hours. c. The approximate number of labor hours is when the number of cubic feet moved is 0 cubic feet is b, hours, O D. For each increase of one labor hour, the number of cubic feet moved is expected to increase by b,. c. Interpret the meaning of the slope, b, in this problem. Choose the correct answer below. O A. The approximate number of cubic feet moved when the number of labor hours is 0 hours is b. O B. For each increase of one cublc foot moved, the number of labor hours is expected to Increase by b, hours O c. The approximate number of labor hours is when the number of cubic feet moved is 0 cubic feet is b. hours O D. For each increase of one labor hour, the number ocubic feet moved is expected to increase by b. d. Predict the mean labor hours for moving 400 cubic feet. hours (Round to two decirmal places as needed.) e. What should you tell the owner of the moving company about the relationship between cubic feet moved and labor hours? O A. As expected, the labor hours are affected by the amount to O B. As the labor hours increase, the amount to be moved decreases. As expected, the amoun O C. As the amount to be moved increases, the labor hours decrease. As expected, the labor hours are affected by the amount to be moved. O D. As expected, the labor hours are not affected by the amount to be moved moved. As the amount to be moved increasees, the labor hours increase. be moved is affected by the labor hours. Data Table Labor Hours Cubic Feet Moved 555 21.75 613 25.00 626 21.75 524 21.50 760 31.25 840 32.50 582 21.75 733 29.50 17.25 468 388 15.50 29.25 711 592 20.25 312 11.25 509 16.50 492 19.75 325 9.50 454 15.50 253 8.75 714 30.00 513 20.00 Print Done X

Answer 1

a) The scatterplot is obtained and attached below. The correct answer is option (d)

b) Using the least squares method, the regression coefficients b0 and b1 are obtained as b0 = -3.134 and

b1 =0.044 (Rounded to three decimal places)

So, the least squares regression equation is y_hat = -3.134 + 0.044 x; where y_hat = predicted value of the labor hours and x = given cubic foot moved.

c) The correct answer is option (b) -- for each increase of one cubic foot moved, the number of labor hours is expected to increase by b1 hours. This is the correct interpretation of the slope b1.

d) The mean labor hours for moving 400 cubic feet is obtained by putting x = 400 in the obtained linear regression equation in part (b), it is obtained to be -3.134+(0.044*400) = 14.47 (rounded to 2 decimal places)

e) The correct answer is option (a) -- as expected, the labor hours are affected by the amount to be moved. As the amount to be moved increases, the labor hours increase. This can be justified from the obtained scatterplot which shows a moderately strong positive linear relationship between the two variables.

(The answers and graph are obtained using R-software. Code and output are attached below for verification).

X R Console > -3.133#x=cubic feet moved y=labor hours 1-3.133 > x=c(555,613, 626,524,760,840,582, 733,468,388,711,592,312 > y=c(21.75,25, 21.75,21.5,31.25,32.5,21.75,29.5,17.25,15. > plot (x,y) > lm (y x) R Graphics: Device 2 (ACTIVE) Call lm (formula = y - x) Coefficients (Intercept 0.04389 -3.13363 30 >3.134+ (0.044 400) [1] 14.466 > 25 20 O 400 300 500 600 700 800 X