Econ 120B Ramu RamanathanWinter 1998 Second Midterm (30%)Your name (please print it) ___________________________________Your Student Id. (NOT Soc. Sec. no.)____________________________DO NOT TURN THE PAGE UNTIL EVERYONE HAS RECEIVEDTHE EXAM AND YOU ARE GIVEN THE SIGNAL TO START.ALSO, YOU MUST STOP WRITING WHEN YOU ARE ASKEDTO DO SO (YOU WILL BE GIVEN A 2 MINUTE WARNING).TEN POINTS WILL BE DEDUCTED FOR EACH MINUTE OFEXTRA TIME IT TAKES YOU TO STOP WRITING.If you use a pencil, you forfeit the right to complain about gradingUNLESS YOU PICK UP THE EXAM FROM THE TA FROMHIS/HER OFFICE AND LOOK AT THE GRADING BEFORELEAVING THE OFFICE.Make sure that all pages (1 through 4) are there. Read the questionscarefully and make sure that you do not misunderstand them. If youget stuck somewhere, don’t waste time but move on.IN THE HYPOTHESIS TESTING PARTS, DON’T ASK MEWHETHER THE TEST IS ONE-SIDED OR TWO-SIDED. YOUHAVE TO FIGURE THAT OUT FOR YOURSELF FROM THEINFORMATION PROVIDED.I CONSIDER CHEATING AS A VERY SERIOUS MATTER ANDWILL GIVE AN F IN THE COURSE TO ANY ONE CHEATINGAND ALSO REFER HIM/HER TO THE DEAN FORDISCIPLINARY ACTION.MAXIMUM NUMBER OF POINTS = 50- 2 -I.The Registrar’s Office at UCSD supplied me with the data for 427 first year undergraduate studentson the GPA in college (COLGPA, the dependent variable), GPA in high school (HSGPA), VerbalSAT scores (VSAT), and math SAT scores (MSAT). Three alternative models were estimated andthe results are in the following table. Values in parentheses are standard errors. Model A usedHSGPA for X, Model B used VSAT, and Model C used MSAT.------------------------------------------------------------------Variables Model A Model B Model C------------------------------------------------------------------αˆ) constant 0.921 1.997 1.628(0.204) (0.141) (0.151)βˆ) HSGPA 0.524(0.057)βˆ) VSAT 0.00157(0.00028)βˆ) MSAT 0.0020(0.00026)------------------------------------------------------------------ESS 103.994 115.837 109.180TSS 124.599 124.599 124.599------------------------------------------------------------------I.a (6 points) In a regression model of the type specified in Assumption 1, indicate two things thatthe goodness of fit (R2) measures.I.b (10 points) For each model, compute the goodness of fit measure. Do the values indicate agood fit or not? Which model is the "best" and why?- 3 -I want to test Model A only___ ___________________ for overall goodness of fit.I.c (2 points) State the null and alternative hypotheses.I.d (4 points) Compute the test statistic and state its distribution under the null, including thenumerical value(s) of the degrees of freedom (d.f.).I.e (10 points) For Model A only______________________ test whether each of the regression coefficients is zero or not(use 1 percent level of significance). Be sure to state the null and alternative hypotheses, thetest statistic and its distribution, including the d.f., the critical value (or range) and the cri-terion for rejection. Are the coefficients significantly different from zero or not?I.f (5 points) Suggest a more general multiple regression model__________________________________________ that is likely to be better than allof the above models. Explain "better" in what sense.- 4 -II.A company claims that the average breaking point (µµ) of its suitcases is over________ 300 lbs. A randomsample of 9 suitcases was tested and it was found that the sample average x__was 305 and the samplevariance was 100. Assuming that the breaking strengths are normally distributed test thecompany’s claim by following the steps given below.II.a (5 points) Compute the test statistic and state its distribution and d.f.II.b (4 points) State the critical value at the 5 percent level of significance, carry out the test, andstate whether the company’s claim is valid or not.II.c (4 points) Construct the 95 percent confidence interval for