The chart below includes information on the Quantity demanded of an item, its pr
ID: 3053687 • Letter: T
Question
The chart below includes information on the Quantity demanded of an item, its price, and consumer’s income for several years. Use this infomraiton to answer the questions that follow.
Fit a multiple regression model to predict the quantity demanded from the price and consumer income. Is the regression significant? Explain. (5 points)
Which variables are most important as predictors of quantity demanded? Explain. (5 points)
Predict the quantity demanded for a price of 86 and income of 1770. (5 points)
Compute the VIFs and examine the t statistics for checking the significance of the individual predictor variables. Is multicollinearity a problem? Explain. (5 points)
Year
Quantity Demanded
Price
Income
2000
40
9
400
2001
45
8
500
2002
50
9
600
2003
55
8
700
2004
60
7
800
2005
70
6
900
2006
65
6
1000
2007
65
8
1100
2008
75
5
1200
2009
75
5
1300
2010
80
5
1400
2011
100
3
1500
2012
90
4
1600
2013
95
3
1700
2014
85
4
1800
Year
Quantity Demanded
Price
Income
2000
40
9
400
2001
45
8
500
2002
50
9
600
2003
55
8
700
2004
60
7
800
2005
70
6
900
2006
65
6
1000
2007
65
8
1100
2008
75
5
1200
2009
75
5
1300
2010
80
5
1400
2011
100
3
1500
2012
90
4
1600
2013
95
3
1700
2014
85
4
1800
Explanation / Answer
Fit a multiple regression model to predict the quantity demanded from the price and consumer income. Is the regression significant? Explain. (5 points)
Quantity Demanded = 82.275 - 5.106 * Price + 0.017 * Income
The regression is significant because the p-value of the F-test is in the order of 10^-8.
Which variables are most important as predictors of quantity demanded? Explain. (5 points)
The Price is most important as predictor of quantity demanded because it has a p-value of 0.0036 and hence the null hypothesis of its coefficient being zero can be rejected.
Predict the quantity demanded for a price of 8.6 and income of 1770. (5 points)
Quantity Demanded
= 82.275 - 5.106 * Price + 0.017 * Income
= 82.275 - 5.106 * 8.6 + 0.017 * 1770
= 68
Compute the VIFs and examine the t statistics for checking the significance of the individual predictor variables. Is multicollinearity a problem? Explain. (5 points)
VIF(Price) = 1/(1-R^2) = 1/(1-0.843) = 6.366
VIF(Income) = 1/(1-R^2) = 1/(1-0.843) = 6.366
Since, VIFs are less than 10, there is no problem of multicollinearity.
SUMMARY OUTPUT Regression Statistics Multiple R 0.975009838 R Square 0.950644183 Adjusted R Square 0.942418214 Standard Error 4.349681563 Observations 15 ANOVA df SS MS F Significance F Regression 2 4372.963244 2186.481622 115.5662188 1.44554E-08 Residual 12 227.0367563 18.9197297 Total 14 4600 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 82.27548314 15.43345969 5.33098118 0.000179064 48.64886316 115.9021031 Price -5.106100796 1.416826869 -3.603898901 0.003619916 -8.193101355 -2.019100237 Income 0.016691929 0.006558634 2.545031305 0.025699462 0.002401893 0.030981965Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.