The president of a company that manufactures drywall wants to
analyze the variables that affect demand for his product. Drywall
is used to construct walls in houses and offices. Consequently, the
president decides to develop a regression model in which the
dependent variable is monthly sales of drywall (in hundreds of 4×8
sheets) and the independent variables are Number of building
permits issued in the county Five-year mortgage rates (in
percentage points) Vacancy rate in apartments (in percentage
points) Vacancy rate in office buildings (in percentage points) To
estimate a multiple regression model, he took monthly observations
from the past 2 years.
a. Determine the regression line.
b. What is the standard error of estimate? Can you use this
statistic to assess the model’s fit? If so, how?
c. What is the coefficient of determination, and what does it tell
you about the regression model?
d. Test the overall validity of the model.
e. Test to determine whether each of the independent variables is
linearly related to drywall demand in this model.
f. Predict next month’s drywall sales with 95% confidence if the
number of building permits is 50, the 5-year mortgage rate is 9.0%,
and the vacancy rates are 3.6% in apartments and 14.3% in office
buildings.
g. Does it appear that the error variable is not normally
distributed? Explain
h. Is the variance of the error variable constant? Explain
i. Is multicollinearity a problem in this model? Why?
j. Use D-W test to determine if there are evidence of positive
first-order autocorrelation?
Summary output of this regression:
Regression Statistics | ||||||||
Multiple R | 0.945307312 | |||||||
R Square | 0.893605915 | |||||||
Adjusted R Square | 0.867007394 | |||||||
Standard Error | 42.63602162 | |||||||
Observations | 21 | |||||||
ANOVA | ||||||||
df | SS | MS | F | Significance F | ||||
Regression | 4 | 244287.8574 | 61071.96436 | 33.59607496 | 1.33794E-07 | |||
Residual | 16 | 29085.28543 | 1817.83034 | |||||
Total | 20 | 273373.1429 | ||||||
Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |
Intercept | -122.7502005 | 152.9559982 | -0.802519692 | 0.434011698 | -447.0024316 | 201.5020306 | -447.0024316 | 201.5020306 |
Permits | 4.775133752 | 0.429532573 | 11.11704688 | 6.1747E-09 | 3.864565373 | 5.68570213 | 3.864565373 | 5.68570213 |
Mortgage | 20.02897754 | 18.05789756 | 1.109153348 | 0.283757601 | -18.25205519 | 58.31001027 | -18.25205519 | 58.31001027 |
A Vacancy | -12.511585 | 7.487834745 | -1.670921625 | 0.11417856 | -28.38508555 | 3.361915558 | -28.38508555 | 3.361915558 |
O Vacancy | 1.009482378 | 3.192951133 | 0.31615967 | 0.755968394 | -5.75927165 | 7.778236405 | -5.75927165 | 7.778236405 |
A.
Regression Line:
Drywall = -122.75 + 4.775*Permits + 20.0289*Mortgage -12.5115*(A vacany) + 1.0095*(O Vacancy)
B.
Std. error of the estimate = 42.636
We use Std. error to calculate the F-statistics which tells us about the model validity.
F-value = MSRegression/(Std. error)2
C.
R2, coefficient of determination = 0.8936
The coefficient of determination is interpreted as the proportion of the variance in the dependent variable that is predictable from the independent variables.
D.
Since the p-value for the F-statistics = 1.3379*10-7 < 0.05
Thus model is significant.
The president of a company that manufactures drywall wants to analyze the variables that affect demand...
The president of a company that manufactures drywall wants to analyze the variables that affect demand for his product. Drywall is used to construct walls in houses and offices. Consequently, the president decides to develop a regression model in which the dependent variable is monthly sales of drywall (in hundreds of 4×8 sheets) and the independent variables are Number of building permits issued in the county Five-year mortgage rates (in percentage points) Vacancy rate in apartments (in percentage points) Vacancy...