Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
14th Edition
ISBN: 9781305506381
Author: James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Publisher: Cengage Learning
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Question
Chapter 4, Problem 4E
(a)
To determine
Statistical significance of the independent variables.
(b)
To determine
The proportion of total variation in sales explained by the regression equation.
(c)
To determine
Overall explanatory power of the model using F-test.
(d)
To determine
Additional statistical information that is useful in the evaluation of the regression model.
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Suppose the Sherwin-Williams Company has developed the following multiple regression model, with paint sales Y (x 1,000 gallons) as the dependent variable and promotional expenditures A (x $1,000) and selling price P (dollars per gallon) as the independent variables.
Y=α+βaA+βpP+εY=α+βaA+βpP+ε
Now suppose that the estimate of the model produces following results: α=344.585α=344.585, ba=0.102ba=0.102, bp=−11.192bp=−11.192, sba=0.173sba=0.173, sbp=4.487sbp=4.487, R2=0.813R2=0.813, and F-statistic=11.361F-statistic=11.361. Note that the sample consists of 10 observations.
1.) According to the estimated model, holding all else constant, a $1,000 increase in promotional expenditures decrease or increase sales by approximately 102,813 or 11,192 gallons. Similarly, a $1 increase in the selling price decrease or increase sales by approximately 813,11,192 or 102 gallons.
2.)Which of the independent variables (if any) appears to be statistically significant (at the 0.05…
Find the regression equation, letting the first variable be the predictor (x) variable. Using the listed actress/actor ages in various
years, find the best predicted age of the Best Actor winner given that the age of the Best Actress winner that year is 43 years. Is
the result within 5 years of the actual Best Actor winner, whose age was 45 years?
Best Actress
27
30
30
61
30 32 46 28
61
22
43
56 D
Best Actor
42
39
38
45 51
49
59 51
38
57
45
34
Find the equation of the regression line.
y =
+
(Round the constant to one decimal place as needed. Round the coefficient to three decimal places as needed.)
The best predicted age of the Best Actor winner given that the age of the Best Actress winner that year is 43 years is
years
old.
(Round to the nearest whole number as needed.)
Is the result within 5 years of the actual Best Actor winner, whose age was 45 years?
the predicted age is
the actual winner's age.
Water is being poured into a large, cone-shaped
cistern. The volume of water, measured in cm³, is
reported at different time intervals, measured in
seconds. A regression analysis was completed and
is displayed in the computer output.
Regression Analysis: cuberoot (Volume) versus Time
Predictor
Coef
SE Coef
Constant
-0.006 0.00017
-35.294
0.000
Time
0.640
0.000018
35512.6
0.000
s=0.030
R-Sq=1.000 R-sq (adj)=1.000
What is the equation of the least-squares regression
line?
Volume = 0.640 - 0.006(Time)
Volume = 0.640 - 0.006(Time)
Volume = -0.006 + 0.640(Time)
Volume = - 0.006 + 0.640(Time?)
Chapter 4 Solutions
Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
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