# The owner of a moving company

The owner of a moving company typically has his most experienced manager predict the total number of labor hours that will be required to complete an upcoming move. This approach has proved useful in the past, but the owner has the business objective of developing a more accurate method of predicting labor hours. In a preliminary effort to provide a more accurate method, the owner has decided to use the number of cubic feet moved and the number of pieces of large furniture as the independent variables and has collected data for 36 moves in which the origin and destination were within the borough of Manhattan in New York City and the travel time was an insignificant portion of the hours worked. The data are organized and stored in Moving.
a. State the multiple regression equation.
b. Interpret the meaning of the slopes in this equation.
c. Predict the labor hours for moving 500 cubic feet with two large pieces of furniture.
d. Perform a residual analysis on your results and determine whether the regression assumptions are valid.
e. Determine whether there is a significant relationship between labor hours and the two independent variables (the number of cubic feet moved and the number of pieces of large furniture) at the 0.05 level of significance.
f. Determine the p-value in (e) and interpret its meaning.
g. Interpret the meaning of the coefficient of multiple determinations in this problem.
i. At the 0.05 level of significance, determine whether each independent variable makes a significant contribution to the regression model. Indicate the most appropriate regression model for this set of data.
j. Determine the p-values in (i) and interpret their meaning.
k. Construct a 95% confidence interval estimate of the population slope between labor hours and the number of cubic feet moved. How does the interpretation of the slope here differ from that in Problem 13.44 on page 501?
l. Compute and interpret the coefficients of partial determination.

# The owner of a moving company

The owner of a moving company typically has his most experienced manager predict the total number of labor hours that will be required to complete an upcoming move. This approach has proved useful in the past, but the owner has the business objective of developing a more accurate method of predicting labor hours. In a preliminary effort to provide a more accurate method, 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 in which the origin and destination were within the borough of Manhattan in New York City and the travel time was an insignificant portion of the hours worked. The data are organized and stored in Moving. For (a) through (k), do not include an interaction term.
a. State the multiple regression equation for predicting labor hours, using the number of cubic feet moved and whether there is an elevator.
b. Interpret the regression coefficients in (a).
c. Predict the labor hours for moving 500 cubic feet in an apartment building that has an elevator and construct a 95% confidence interval estimate and a 95% prediction interval.
d. Perform a residual analysis on the results and determine whether the regression assumptions are valid.
e. Is there a significant relationship between labor hours and the two independent variables (cubic feet moved and whether there is an elevator in the apartment building) at the 0.05 level of significance?
f. At the 0.05 level of significance, determine whether each independent variable makes a contribution to the regression model. Indicate the most appropriate regression model for this set of data.
g. Construct a 95% confidence interval estimate of the population slope for the relationship between labor hours and cubic feet moved.
h. Construct a 95% confidence interval estimate for the relationship between labor hours and the presence of an elevator.
i. Compute and interpret the adjusted r2.
j. Compute the coefficients of partial determination and interpret their meaning.
k. What assumption do you need to make about the slope of labor hours with cubic feet moved?
1. 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.
m. On the basis of the results of (f) and (1), which model is most appropriate? Explain. regression model. Indicate the most appropriate regression model for this set of data.

# The owner of a moving company

The owner of a moving company typically has his most experienced manager predict the total number of labor hours that will be required to complete an upcoming move. This approach has proved useful in the past, but the owner has the business objective of developing a more accurate method of predicting labor hours. In a preliminary effort to provide a more accurate method, the owner has decided to use the number of cubic feet moved as the independent variable and has collected data for 36 moves in which the origin and destination were within the borough of Manhattan in New York City and in which the travel time was an insignificant portion of the hours worked. The data are stored in Moving.
a. Construct a scatter plot.
b. Assuming a linear relationship, use the least-squares method to determine the regression coefficients b0 and b1.
c. Interpret the meaning of the slope, b1, in this problem.
d. Predict the labor hours for moving 500 cubic feet.

# The owner of a moving company

The owner of a moving company typically has his most experienced manager predict the total number of labor hours that will be required to complete an upcoming move. This approach has proved useful in the past, but the owner has the business objective of developing a more accurate method of predicting labor hours. In a preliminary effort to provide a more accurate method, the owner has decided to use the number of cubic feet moved and the number of pieces of large furniture as the independent variables and has collected data for 36 moves in which the origin and destination were within the borough of Manhattan in New York City and the travel time was an insignificant portion of the hours worked. The data are organized and stored in Moving .
a. State the multiple regression equation.
b. Interpret the meaning of the slopes in this equation.
c. Predict the mean labor hours for moving 500 cubic feet with two large pieces of furniture.
d. Perform a residual analysis on your results and determine whether the regression assumptions are valid.
e. Determine whether there is a significant relationship between labor hours and the two independent variables (the number of cubic feet moved and the number of pieces of large furniture) at the 0.05 level of significance.
f. Determine the p value in (e) and interpret its meaning.
g. Interpret the meaning of the coefficient of multiple determination in this problem.
i. At the 0.05 level of significance, determine whether each independent variable makes a significant contribution to the regression model. Indicate the most appropriate regression model for this set of data.
j. Determine the p values in (i) and interpret their meaning.
k. Construct a 95% confidence interval estimate of the population slope between labor hours and the number of cubic feet moved. How does the interpretation of the slope here differ from that in Problem 12.44 on page 443?
l. What conclusions can you reach concerning labor hours?

# The owner of a moving company

The owner of a moving company typically has his most experienced manager predict the total number of labor hours that will be required to complete an upcoming move. This approach has proved useful in the past, but the owner has the business objective of developing a more accurate method of predicting labor hours. In a preliminary effort to provide a more accurate method, 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 in which the origin and destination were within the borough of Manhattan in New York City and the travel time was an insignificant portion of the hours worked. The data are organized and stored in Moving . For (a) through (j), do not include an interaction term.

a. State the multiple regression equation for predicting labor hours, using the number of cubic feet moved and whether there is an elevator.

b. Interpret the regression coefficients in (a).

c. Predict the mean labor hours for moving 500 cubic feet in an apartment building that has an elevator and construct a 95% confidence interval estimate and a 95% prediction interval.

d. Perform a residual analysis on the results and determine whether the regression assumptions are valid.

e. Is there a significant relationship between labor hours and the two independent variables (cubic feet moved and whether there is an elevator in the apartment building) at the 0.05 level of significance?

f. At the 0.05 level of significance, determine whether each independent variable makes a contribution to the regression model. Indicate the most appropriate regression model for this set of data.

g. Construct a 95% confidence interval estimate of the population slope for the relationship between labor hours and cubic feet moved.

h. Construct a 95% confidence interval estimate for the relationship between labor hours and the presence of an elevator.

i. Compute and interpret the adjusted r2.

j. What assumption do you need to make about the slope of labor hours with cubic feet moved?

k. 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.

l. On the basis of the results of (f) and (k), which model is most appropriate? Explain.

m. What conclusions can you reach concerning the effect of the number of cubic feet moved and whether there is an elevator on labor hours?

# The owner of a moving company

The owner of a moving company typically has his most experienced manager predict the total number of labor hours that will be required to complete an upcoming move. This approach has proved useful in the past, but the owner has the business objective of developing a more accurate method of predicting labor hours. In a preliminary effort to provide a more accurate method, the owner has decided to use the number of cubic feet moved as the independent variable and has collected data for 36 moves in which the origin and destination were within the borough of Manhattan in New York City and in which the travel time was an insignificant portion of the hours worked. The data are stored in Moving.

a. Construct a scatter plot.

b. Assuming a linear relationship, use the least squares method to determine the regression coefficients b0 and b1.

c. Interpret the meaning of the slope, b1, in this problem.

d. Predict the mean labor hours for moving 500 cubic feet. e. What should you tell the owner of the moving company about the relationship between cubic feet moved and labor hours?

# The owner of a moving company

The owner of a moving company would like to be able to predict the number of hours required to complete a move by using the number of cubic feet of items moved. He has collected data for 36 moves in which the origin and destination were within the city limits of Coral Gables and in which the travel time was an insignificant portion of the hours worked.Q-1a: What is the slope of the least squares regression line

# The owner of a moving company

The owner of a moving company typically has his most experienced manager predict the total number of labor hours that will be required to complete an upcoming move. This approach has proved useful in the past, but he would like to be able to develop a more accurate method of predicting labor hours by using the number of cubic feet moved. In a preliminary effort to provide a more accurate method, he has collected data for 36 moves in which the origin and destination were within the borough of Manhattan in New York City and in which the travel time was an insignificant portion of the hours worked. The data are stored in the file moving.xls.

a. Construct a scatter plot.

b. Assuming a linear relationship, use the least-squares method to find the regression coefficients b0 and b1.

c. Interpret the meaning of the slope, b1 , in this problem.

d. Predict the mean labor hours for moving 500 cubic feet.