a. Find the least squares prediction equation. b. Use an F-test to investigate the usefulness of the model specified in part a. Use a = .01 and state your conclusion in the context of the problem. c. Test Ho: B2 = 0 versus Ha: 32 # 0 using a = .05. What do the results of your test suggest about the magnitude of the effects of x2 on labor costs? d. Find R² and interpret its value in the context of the problem.
a. Find the least squares prediction equation. b. Use an F-test to investigate the usefulness of the model specified in part a. Use a = .01 and state your conclusion in the context of the problem. c. Test Ho: B2 = 0 versus Ha: 32 # 0 using a = .05. What do the results of your test suggest about the magnitude of the effects of x2 on labor costs? d. Find R² and interpret its value in the context of the problem.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Please do only the last three
![12.24 COST ANALYSIS FOR A SHIPPING DEPARTMENT. Multiple regression is used by
SHIP
accountants in cost analysis to shed light on the factors that cause costs to be incurred and the
magnitudes of their effects. Sometimes, it is desirable to use physical units instead of cost as the
dependent variable in a cost analysis (e.g., if the cost associated with the activity of interest is a
function of some physical unit, such as hours of labor). The advantage of this approach is that the
regression model will provide estimates of the number of labor hours required under different
circumstances, and these hours can then be costed at the current labor rate (Horngren and Datar,
Cost Accounting, 2014). The sample data shown in the table above have been collected from a firm's
accounting and production records to provide cost information about the firm's shipping department.
These data are saved in the file. Consider the model
------
y = Bo + B₁x1 + B₂x2 + 3x3 + ε
a. Find the least squares prediction equation.
b. Use an F-test to investigate the usefulness of the model specified in part a. Use a = .01 and
state your conclusion in the context of the problem.
c. Test Ho: B₂ = 0 versus Ha: B20 using a = .05. What do the results of your test suggest
about the magnitude of the effects of x2 on labor costs?
d. Find R² and interpret its value in the context of the problem.
e. If shipping department employees are paid $7.50 per hour, how much less, on average, will it
cost the company per week if the average number of pounds per shipment increases from a
level of 20 to 21? Assume that ₁ and 2 remain unchanged. Your answer is an estimate of
what is known in economics as the expected marginal cost associated with a 1-pound increase
in 23.
f. With what approximate precision can this model be used to predict the hours of labor? [Note:
The precision of multiple regression predictions is discussed in Section 12.49.]
g. Can regression analysis alone indicate what factors cause costs to increase? Explain.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2e68f9cd-bde5-4bf0-be95-86dc6cd14d49%2Ff0539614-5439-4385-9eb1-c392d734d648%2Fvu24c2_processed.png&w=3840&q=75)
Transcribed Image Text:12.24 COST ANALYSIS FOR A SHIPPING DEPARTMENT. Multiple regression is used by
SHIP
accountants in cost analysis to shed light on the factors that cause costs to be incurred and the
magnitudes of their effects. Sometimes, it is desirable to use physical units instead of cost as the
dependent variable in a cost analysis (e.g., if the cost associated with the activity of interest is a
function of some physical unit, such as hours of labor). The advantage of this approach is that the
regression model will provide estimates of the number of labor hours required under different
circumstances, and these hours can then be costed at the current labor rate (Horngren and Datar,
Cost Accounting, 2014). The sample data shown in the table above have been collected from a firm's
accounting and production records to provide cost information about the firm's shipping department.
These data are saved in the file. Consider the model
------
y = Bo + B₁x1 + B₂x2 + 3x3 + ε
a. Find the least squares prediction equation.
b. Use an F-test to investigate the usefulness of the model specified in part a. Use a = .01 and
state your conclusion in the context of the problem.
c. Test Ho: B₂ = 0 versus Ha: B20 using a = .05. What do the results of your test suggest
about the magnitude of the effects of x2 on labor costs?
d. Find R² and interpret its value in the context of the problem.
e. If shipping department employees are paid $7.50 per hour, how much less, on average, will it
cost the company per week if the average number of pounds per shipment increases from a
level of 20 to 21? Assume that ₁ and 2 remain unchanged. Your answer is an estimate of
what is known in economics as the expected marginal cost associated with a 1-pound increase
in 23.
f. With what approximate precision can this model be used to predict the hours of labor? [Note:
The precision of multiple regression predictions is discussed in Section 12.49.]
g. Can regression analysis alone indicate what factors cause costs to increase? Explain.
Transcribed Image Text:Regression Analysis: Labor versus Pounds, PctShip, AveWt
Regression Equation
Labor = 131.9 +2.73 Pounds + 0.0472 PctShip - 2.587 AveWt
Coefficients
Term
Coef SE Coef T-Value P-Value VIF
Constant
131.9
25.7
Pounds
2.28
2.73
PctShip 0.0472 0.0933
AveWt
Model Summary
5.13 0.000
1.20 0.248 2.25
0.51 0.620 1.09
-2.587 0.643 -4.03 0.001 2.17
S R-sq R-sq(adj) R-sq(pred)
72.70%
63.04%
9.81035 77.01%
Analysis of Variance
Source
DF Adj ss
Regression 3 5158.31
Pounds
1
138.19
1
24.62
1 1559.32 1559.32
16 1539.89
96.24
19 6698.20
PctShip
AveWt
Error
Total
Adj MS F-Value P-Value
1719.44 17.87 0.000
138.19 1.44 0.248
24.62
0.26
0.620
16.20
0.001
Fits and Diagnostics for Unusual Observations
Fit Resid Std Resid
-2.59 R
Obs Labor
13 50.00 73.33 -23.33
R Large residual
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