LTZ Automotive is trying to estimate the unit cost of designing and producing a
ID: 3155358 • 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.
(a) 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?
(b) What is multicollinearity? Is there a problem with multicollinearity in this application? If so, what should be done?
Explanation / Answer
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).
Here dependent variable y is price and independent variables are horsepower, time from zero to 60 miles per hour, top speed, miles per gallon, type of transmission.
(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.
Here we have to fit regression.
We can fit regression using MINITAB.
steps :
Enter data in MINITAB sheet --> Stat --> Regression --> Regression --> Response : y --> Predictors : x1,x2 and x3 --> Options : click on variance inflation factors --> ok --> Results : select second option --> ok --> ok
Regression Analysis: y versus x1, x2, x3
The regression equation is
y = 99.6 - 6.65 x1 - 0.030 x2 - 0.84 x3
Predictor Coef SE Coef T P VIF
Constant 99.56 65.16 1.53 0.177
x1 -6.646 2.885 -2.30 0.061 1.3
x2 -0.0299 0.2816 -0.11 0.919 3.2
x3 -0.840 1.191 -0.71 0.507 3.1
S = 6.74674 R-Sq = 62.9% R-Sq(adj) = 44.3%
PRESS = 1075.50 R-Sq(pred) = 0.00%
Analysis of Variance
Source DF SS MS F P
Regression 3 462.90 154.30 3.39 0.095
Residual Error 6 273.11 45.52
Total 9 736.02
Assume level of significance = alpha = 10% = 0.1
For overall model F test statistic = 3.39 and P-value = 0.095
P-value < alpha
At 10% level of significance the overall model is significant.
At 10% level of significance P-value for x2 and x3 are 0.919 and 0.507 respectively.
So x2 and x3 are insignificant.
while x1 has P-value 0.061 which is < alpha.
x1 is significant.
We have to delete x2 and x3 which are insignificant.
x1 is significant therefore included x1 in the model.
Therefore by deleting x2 and x3 the model is,
Regression Analysis: y versus x1
The regression equation is
y = 86.3 - 7.78 x1
Predictor Coef SE Coef T P
Constant 86.31 14.69 5.88 0.000
x1 -7.778 2.401 -3.24 0.012
S = 6.30836 R-Sq = 56.7% R-Sq(adj) = 51.3%
PRESS = 709.237 R-Sq(pred) = 3.64%
Analysis of Variance
Source DF SS MS F P
Regression 1 417.65 417.65 10.50 0.012
Residual Error 8 318.36 39.80
Total 9 736.02
What is the coefficient of determination for this equation? What does it tell us?
R2 = 56.7%
It expresses the proportion of the variation in y which is explained by variable in x.
(b) What is multicollinearity? Is there a problem with multicollinearity in this application? If so, what should be done?
In statistics, multicollinearity (also collinearity) is a phenomenon in which two or more predictor variables in a multiple regression model are highly correlated, meaning that one can be linearly predicted from the others with a substantial degree of accuracy.
If VIF > 10 then there is high multicollinearity.
Here VIF for each variable is < 10.
There is no sign of multicollinearity.
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