Auto, Inc., a fictional automobile manufacturer, is interested in estimating the
ID: 3232899 • Letter: A
Question
Auto, Inc., a fictional automobile manufacturer, is interested in estimating the value derived from a proposed Strategic Alternative (SA). The SA, posed by the CEO of the company, is to acquire an elite, high-end auto company where the average retail price of a car is $80,000. As part of this task, the acquisition team develops a three-year market analysis to determine if adequate market demand exists for luxury automobiles. The team chooses to use the predictive power of regression analysis to help make these projections.
The first step in this process is to understand what drives total market demand for elite, high-end luxury automobiles. After analyzing the industry, the group hypothesizes that gross domestic product, or GDP, is a key predictor of market demand for these automobiles.
To gather historical GDP data, the team turns to online databases located on the Federal Reserve Board website.To gather data on new vehicle sales for elite, high-end luxury cars, it uses the Bureau of Labor Statistics' online databases on new vehicle car sales. (The GDP data is in billions of dollars and the sales data is in thousands of units.)
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.831453
R Square
0.691314
Adjusted R Square
0.652728
Standard Error
251.102335
Observations
10
ANOVA
df
SS
MS
F
Significance F
Regression
1
1129665.838
1129665.84
17.9163069
0.0028655
Residual
8
504419.0623
63052.3828
Total
9
1634084.9
Coefficients
Standard Error
t Stat
P-value
Intercept
739.44976
519.58568
1.42315
0.19250
GDP (in $billions)
0.28527
0.06740
4.23277
0.00287
a) Is GDP a valid predictor of sales? How do you know?
b) If the GDP is at 12,000 billion dollars, how many thousands of units of cars would you expect to be sold?
c) Interpret b1.
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.831453
R Square
0.691314
Adjusted R Square
0.652728
Standard Error
251.102335
Observations
10
ANOVA
df
SS
MS
F
Significance F
Regression
1
1129665.838
1129665.84
17.9163069
0.0028655
Residual
8
504419.0623
63052.3828
Total
9
1634084.9
Coefficients
Standard Error
t Stat
P-value
Intercept
739.44976
519.58568
1.42315
0.19250
GDP (in $billions)
0.28527
0.06740
4.23277
0.00287
Explanation / Answer
here level of significance alpha is not mentioned , let it is alpha=0.05 ( generally alpha-0.05 is taken)
(a) Yes, GDP is a valid predictor of sales. since p-value of GDP in regression analysis is 0.00287 is less than alpha=0.05, so it is significant at 5% level of significance
(b) the regression equation here is
cars=739.45+0.2853*GDP
for GDP=12000, the cars==739.45+0.2853*12000=4163.05 thosand
answer is 4163.05 thosand
(c) here the regresssion equation y=b0+b1*x is fitted and the fitted equation is
cars(y)=739.45+0.2853*GDP(x)
here b0=739.45 and b1=0.2853
the p-value of b1 is 0.00287 and less than alpha=0.05, so it is significant at 5% level of significance. so GDP is signifanct for sale of number of cars units
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