Question

The following are regression results where Car Price is the dependent variable:

Regression Statistics

?2=0.446R2=0.446 Adjusted ?2=0.441R2=0.441 Observations = 804

Independent Variables	Coefficients	Standard Error	t Stat	P-value
Intercept	6758.76	1876.967	3.601	0.000
Mileage	-0.17	0.032	-5.326	0.000
Cylinder	3792.38	683.180	5.551	0.000
Liter	-787.22	867.062	-0.908	0.364
Doors	-1542.75	320.456	-4.814	0.000
Cruise	6289.00	657.992	9.558	0.000
Sound	-1993.80	571.776	-3.487	0.001
Leather	3349.36	597.681	5.604	0.000

Car Price is measured in dollars. The independent variables are:

• Mileage: number of miles the car has been driven
• Cylinder: number of cylinders in the engine
• Liter: a more specific measure of engine size
• Doors: number of doors
• Cruise: dummy variable representing whether the car has cruise control (1 = cruise, 0 = no cruise)
• Sound: dummy variable representing whether the car has upgraded speakers (1 = upgraded, 0 = standard)
• Leather: dummy variable representing whether the car has leather seats (1 = leather, 0 = cloth)

Question 17

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This model (set of independent variables) explains approximately how much of the variation in car prices in this dataset?

Select one:

a. 80.480.4

b. 44.144.1

c. 1−0.441=55.91−0.441=55.9

d. 44.644.6

Question 18

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What is true about the estimated coefficients?

Select one:

a. The "Mileage" coefficient is unexpectedly small compared to the others, suggesting that miles driven is unimportant in the selling price of a used car.

b. The "Sound" coefficient is unexpectedly negative, suggesting that cars with upgraded speakers are associated with a lower selling price.

c. The negative "Door" coefficient indicates that more doors on a car reduce the car's mileage.

d. The "Mileage" coefficient is unexpectedly negative, since higher miles driven should be associated with a higher selling price.

Question 19

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The results from the ?t-statistics and ?p-values suggests that

Select one:

a. Mileage, Liter, Doors, and Sound are all insignificant since the ?t-stats are negative.

b. Only the coefficient for "Liter" is statistically insignificant. All of the other coefficients are statistically significant at the 1% level.

c. Mileage, Cylinder, Doors, Cruise, and Leather are all insignificant since the ?p-values are zero, meaning unrelated to car price.

d. "Liter" is the only statistically significant estimate since it's ?p-value is 36.4%.

Question 20

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Which of the following statements is correct, based on the regression results above?

Select one:

a. Every additional mile driven increases the price of the car by $0.17

b. Since the "Liter" coefficient is insignificant, the true effect is actually +787.22 and not -787.22

c. Having four doors instead of two is associated with more than a $3,000 lower price, everything else equal.

d. Cars with cruise control have about 6,300 fewer miles on them than cars without cruise control, everything else equal.

Answer 1

1. 44.6446

{ Explained variation is given by the value of multiple R square.}

2.Mileage coefficient is unexpectedly negative,since higher miles driven should bed associated with higher selling price.

{Negative coefficient indicates a negative relationship between dependent variable car Price and independent variable mileage . Usually the relationship between these two variables are direct and positive. In our result, its negative.)

3. Only coefficient for litre is statistically insignificant.All the other coefficients are statistically significant at 1 percent level.

{ coefficients are significant at 1 percent level if their value is lower than 0.01.Here p values of all the variables except litre are zero ( less than one) . only p value of litre is greater than 0.01. Therefore, only litre is insignificant.}

4) Having two doors instead of four is associated with more than $ 3000 lower Price, everything else equal.

{Door coefficient is -1542.75 which means that having a door less will decrease the price by 1542.75 $

Now, having two doors instead of four will reduce the price by 3085.5 $}