LTZ Automotive is trying to estimate the unit cost of designing and producing a
ID: 3157173 • Letter: L
Question
LTZ Automotive is trying to estimate the unit cost of designing and producing a new sports car which they think will be a big hit amongst sports car enthusiasts. To develop the cost estimate, they decided to use the parametric approach meaning they need to analyze historical information. LTZ approached ADS (Automotive Data Sources) to purchase the appropriate data. ADS was able to provide the following data on horsepower, time from zero to 60 miles per hour, top speed, miles per gallon, type of transmission, and cost (development and production) in thousands of dollars for 10 popular sports cars (SPORTS CAR DATA.MTW).
Horse- Zero to 60 Top Speed Miles per Trans- Price
Sports Car power (Seconds) Miles/Hour Gallon mission ($1000s)
A 240 6.0 120 24.6 Automatic 38.4
B 300 5.7 170 16.8 Manual 41.4
C 400 4.8 160 14.0 Manual 54.8
D 240 6.9 140 18.0 Manual 25.8
E 190 7.1 139 24.0 Automatic 25.6
F 320 5.7 159 16.3 Manual 43.7
G 320 5.3 155 18.8 Automatic 48.2
H 300 6.0 155 18.7 Automatic 40.8
I 320 7.6 150 17.5 Automatic 38.1
J 255 5.5 158 17.0 Manual 35.0
(a) Develop an estimated regression equation to predict the price. Is your model significant? Are all the variables significant? If not, which ones are and which ones are not? Explain.
(b) Delete any independent variable that is not significant and provide your recommended regression equation. What is the coefficient of determination for this equation? What does it tell us?
(c) What is multicollinearity? Is there a problem with multicollinearity in this application? If so, what should be done?
(d) Suppose the specified characteristics of this new sports car are as follows:
Horsepower: 350 Zero-to-60: 4.0 seconds Top Speed: 170 mph
MPG: 22.5 Transmission: Automatic
What is the estimated unit cost for this proposed sports car and what is the range of uncertainty for this unit cost?
Explanation / Answer
a.
Regression Equation
trans-mission
automatic price ($1000s) = -24.2 + 0.1608 Horse Power - 3.608 zero - 60 (sec)
+ 0.0829 top speed + 1.424 miles/ gallon
manual price ($1000s) = -24.4 + 0.1608 Horse Power - 3.608 zero - 60 (sec)
+ 0.0829 top speed + 1.424 miles/ gallon
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant -24.2 26.3 -0.92 0.411
Horse Power 0.1608 0.0205 7.83 0.001 8.20
zero - 60 (sec) -3.608 0.775 -4.66 0.010 2.58
top speed 0.0829 0.0598 1.39 0.238 4.04
miles/ gallon 1.424 0.544 2.62 0.059 18.26
trans-mission
manual -0.20 1.84 -0.11 0.919 5.30
From the p-value, we can see that top speed, and manual level of the categorical variable transmission is not significant.
b. Removing the non significant variable new regression equation is
price ($1000s) = -5.23 + 0.1592 Horse Power - 3.777 zero - 60 (sec) + 1.152 miles/ gallon
Coefficient of determination = 0.9857
It tells us that the model is very good.
c. Multicollinearity is problem appears when independent variables are dependent on each other.
Here problem of multicollienarity is present. So, the dependent variable will be dropped.
d. Estimated price is $ 63.781
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