Regression Models using Cross Section Data

Use the data set in DATA_ASSIGNMENT which contains information on the price and characteristics of cars sold in Australia. The variable Sale Price is the retail sale price of a car in Australia in Australian dollars, Length is the length of the car in cm, Weight is the weight of a car in kilograms, Horsepower is the power measure of a car, Luggage size is the amount of luggage space the car has and the dummy variables (Sedan, Hatchback, SUV, Wagon, Luxury, Sport) show the type of the car.

(i) Present the descriptive statistics of the variables Sale Price, Length and Weight. Comment on the means and measures of dispersion of the variables.

(ii) Estimate the following simple regression model of sale price on length.

SalePrice = β₀+ β₁length + u

Write down the sample regression function and interpret the coefficient estimates.

(iii) Now estimate the following simple regression model with a log-log specification, log(SalePrice) = β₀ + β₁log(length) + u

Report your regression results in a sample regression function. Interpret the estimated coefficient of log(length). What did you expect this coefficient to be before the estimation and is the sign of this estimate what you expect it to be?

(iv) A model that relates the car sale price to the car length and car weight is:

SalePrice = β₀ + β₁length + β₁weight + u

Report your results in a sample regression function. What can you conclude regarding comparison of the goodness of fit of this regression model versus the regression model in part (ii)?

(v) Now re-estimate the equation in (iv) but using the log of each variable. That is, estimate the model,

log(SalePrice) = β₀+ β₁log(length) + β₂log(weight) + u

Report the results in a sample regression function. What is the estimated elasticity of sale pricewith respect to weight? Test whether it is statistically significant at 1% level.

(vi) Using the estimated model in (v), test whether length has a negative effect on sale price at 1% level of significance.

(vii) Add the variables horsepower and luggagesize to the log-log equation in (v) and estimate the following model.

log(SalePrice) = β₀+ β₁log(length) + β₂log(weight) + β₃horsepower + β₄luggagesize + u

Test whether either of these variables horsepower and luggagesizeare individually significant at 1% level?Test if they are jointly significant at 5% level?

(viii) Test the overall significance of the model you estimated in part (vii) at 1% level of significance.

(ix) Suppose you want to test whether luxury cars are more expensive than other type of cars. Specify a regression model which will enable you to test such a hypothesis using the model in (v) as a base. Report your results in a sample regression function and perform the hypothesis test at 5% level of significance. What would you infer?

Attachment:- DATA.rar