Page 1Page 2Page 31UCSD Professor Eli BermanEconomics 120B Winter 2008Problem Set #3due Thursday, Feb.281. The data set auto.dta contains data describing new car models sold in the US in 1978. Variablesinclude price (in $), weight (lbs), foreign (0= domestic, 1= foreign), mpg (miles per gallon). You candownload it from http://www.stata-press.com/data/r9/auto.dta then read it into Stata by giving thecommand “use auto.dta" .Create a variable which indicates if a car is domestically produced using the Stata commandgenerate domestic = 1-foreignEstimate the following three equations:a) What proportion of the variation in price is explained by the right hand side variables in equation(L)? 2 2 b) Test the hypothesis that $ is zero in equation (RL) against the alternative that $ is not zero at aRL RLlevel of significance " of .05. 12c) Test the joint hypothesis that both $ , and $ are zero in equation (RL) against the alternative thatRL RLthey are not both zero at " = .05. Report the test statistic.d) Which are heavier on average, domestic or foreign cars (in this sample)? Show how you can use theomitted variable bias formula and the results of the estimated equations (S) and (L) to calculate thedifference in weight between the averae domestic car and the average foreign car. e) A 1978 Volvo 260 weighed 3170 lbs., was foreign and got 17 miles per gallon in gas mileage. Useequation (RL) to predict how much your father would have had to pay for a new Volvo 260 in 1978.2f) What was the actual price of a Volvo 260 in 1978? What is the sign of the estimated residual for this car from equation (RL)? Was the Volvo 260 overpriced according to your calculations? A fair number of Volvo 260s were sold. How can you explain their popularity?1g) An engineering student looks at your estimate for $ in equation (RL) and asks you if it means he canincrease the value of a car by weighing it down with bags of wet sand in the rear trunk. Can he? 1 If not, how would you explain to the engineering student the interpretation of $ ?2. (This has nothing to do with cars, necessarily) Prove that the R from a regression of Y on X in the sample is the same as the R from a regression of22Y on the predicted value, ì, in the same sample.You can always demonstrate this using some data in Stata. (After a regression the command “predictyhat, xb” will create a variable “yhat” of predicted values.) Of course a demonstration isn’t a proof.33. If all the observations in the sample lie exactly on a horizontal line (parallel to the X axis), what willthe value of the R be from a regression of Y on X ? 2Prove