Question

Problem.2. Because of economic crisis Darth Vader ordered Data Analysis department of the Empire Inc. to analyze the price factors of Star Fighters of different modifications. Data (N=74 obs) on the ion-fuel-economy (mpi), length, weight of carried laser arm (kg), Twin Ion Engine displacement (cubic cm) and Engine origin ( For Empire Inc., variable Foreign =0) were used to find out how the estimate of the price (SM) of Fighters depends on fuel economy. The results are following: reg price log_weight displ mpg price | Coef. Std. Err. t Pt1 (95% Conf. Interval] ------------- ---------------------------------------------------------------- lweight | 5023.735 2455.872 2.05 0.045 124.4043 9923.066 displacement | 15.44883 5.665917 2.73 0.008 4.145633 mpg | -.4944547 _cons / -38135.33 78.29681 20118.82 -0.01 -1.90 0.995 0.062 -156.6923 -78271.28 26.75203 155.7034 2000.621 a. Write regression equation (1 pts) b. Interpret slope coefficients. Do they seem to make sense? Are the coefficients significant (state Null hypothesis)? What does that mean?(9 pts) Using stata outputs presented on the next page conduct the following tests. (State Null hypothesis, write conclusions, propose remedy if necessary). b. Multicollinearity (2.5pts) c. Hetroskedasticity (2.5 pts) d. Being not satisfied with the results and to make sure you are not underestimate the Power of the Dark Side, Dart Vader asked you to additionally figure out whether or not Twin Ion Engine displacement and its Ion-fuel economy do not have joint significant effect on price. What are yours conclusions? (2.5 pts) e. Describe the hypothesis test of primary interest for this study. What is your conclusion? (1 pts) f. To get a BLUE estimator of the power of the dark side, Darth Vader requested to look at additional model specifications. Is here STATA’s results that allow you to come up with a reasonable recommendations? Explain. (2pts)

Answer 1

(a)The estimated regression equation can be written as below-

price = -38135.33+5023.735lweight+15.44886displacement-.4944547mpg

(b)1. Interpretation of coefficients-

when log of weight of the star fighter increases by one unit,the price of the star fighter increases by $5023.735M.

when displacement of the star fighter increases by one unit,the price of the star fighter increases by $15.44886M.

when the miles per gallon of fuel (mpg) of the star fighter increases by one unit,the price of the star fighter decreases by $.4944547M

2.The coefficient of lweight and displacement is significant but the coefficient of mpg and the constant is not significant at 5% level of significance.We conclude this as the given p-value is <0.05 for the first two variables implying that the null hypothesis was rejected but for the remaining two,p -value >0.05 implying that the null hypothesis was not rejected.

The H0(null hypothesis) for each case is

Ho:B=0

H :8 +0
,where $\beta$ is the coefficient corresponding to each variable.

3.This means that we cannot rely on mpg or the constant to estimate the price of the star fighter.We can do away with the two variables.

c.test for heteroscedasicity.

There is no problem of heteroscedasticity as Prob that test statistic given by chi sq=6.95 is greater then critical value is 0.0084<0.05. The H0 is rejected at 5% level of significance.

d. to test for the joint significance of twin-ion engine displacement(displacement) and Ion-fuel economy(mpg),

we interpret the ttest mpg=displacement=0 command.

Prob F-statistic>critical value= 0.0292<0.05 which implies that H0 is rejected at 5% level of significance. here,the H0 was that coefficients of both variables equals zero .We can conclude that the variables, twin-ion engine displacement and Ion-fuel economy are jointly significant.