Name. Department of Economics Ohio Wesleyan University Delaware, Ohio. Robert J. Gitter Econometrics Economics 355 Spring, 2007.

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1 Name Department of Economics Ohio Wesleyan University Delaware, Ohio Robert J. Gitter Econometrics Economics 355 Spring, 2007 Exam I You have one hour for this exam. The exam is worth 12.5% of your grade. The exam is closed book, but calculators are permitted. Please do all your work carehlly and check your calculations before handing your work in. PLEASE SHOW ALL YOUR WORK TO AID IN THE AWARDING OF PARTIAL CREDIT WHERE APPLICABLE. Please check your for data sets for problems 1 and 5. To aid in awarding partial credit, please save your output as a word file, using your name to name the file. Please it to Patti Krebehenne at plkrebeh@,owu.edu so she can print it out.

2 1. (50 poiits) Please open the SPSS file I ed you labeled SchSal. Data are for the 50 states and the District of Columbia, so n=5 1. The variables are: Salary = Average public school teacher salary ($1,000~) Spending = Average spending on education per student ($1,000~) South = 1 if Southern state; 0 if not. a. Please run a simple regression to determine the effect that spending has on salary. Write the regression results (coefficients) below. b. Please interpret the coefficient on spending in terms of the variables. '\MA s, 6 ~h+lk d f 9 I, O,J fi ~l* /3* 4,,+,'4 P P~P~sI,!P& LA *I JA/&/> p, ar k /P q 1,3 ij c. Please test the hypothesis 7d At the.05 level. BP,,jab pejfi'cu> IS!' 6..J L I p.,r,s.lyr ('&Zd, ; LkhIAL..r> / j~ / Q j ~ r b i I d. Please explain what your results in part c mean in terms of the variables.

3 e. $uppose we want to see if salaries on all of these together: spending, whether the state is in the South the effect of spending on salaries is.different in the South, i.e., a multiple regression with each of these Please run such a regression and write your answer (coefficients) belo U f. Please interpret the coefficient on the variable South in terms of the variables. CAe inhddc~% (o,m+r, gkhi Q/' P /. I k,,,~ 1 = %/&/,P, t44.1 0, c%.270 ihfej g. P ease interpret the coefficient on the last variable. (;,q JT*. "j 6 r 9 n*, JUJk~, fmd 14~ 0 hd kkf re LL 9/.e~r&?~ LL,, r,,i >=J3q f J;("/'"< c q kaf r Jvk4 a $ / 0 /*?//*tw PY~ J pp~ J k J ~ ~ d,. ~ d ~ ~ k b j ;I " jn.{ ~ " C ~ J P lp 0 (4 9, ~w/fi,, <J f535 utt"..# /, L7 LfG / t 9 h$+ fld 70 i'? ' 4,Iq 87 3dJk4 ( P?P a r AV s', / N y 4 r/. r,a 4, pp,., Lyh ekb+ /At. pvp lw'n 'A pro J/ nr 'l <)<Ilk f J il,h,rm roy I lqk/ar~$cj? 1. Please test the following hypothesis at the.05 level: Q... X. k] : I=# 3,, = = H,: BZ=Bs=B4=0 '~4 n n,,.i 2. e/ VS. 9 ' i(v LY; 1) '' h*iqihat does the Rsquared tell us in terms of the variables?, Ilu, HA : Ho is false kq~cf i./ j= = %5!% lz 2, *</ 37.?r cd b/l bl j. Please test if we can drop those variables together that were not statistically significant at the.05 level in part e. Show your work. can,/clr~~~i') hf~f \ I

4 2. (10 points) An economist, Jeffrey Woolridge, ran a regression and found. In Price = In nox rooms (Note: the rooms variable is not in In form.) Where: Price = median housing price in a community Nox = amount of nitrogen oxide in parts per million (a pollutant) in the air in the community Rooms= average number of rooms in the house in the community a. Please interpret, in terms of the variab es what the slope on nox tells you? L,,ficy qn.*& 414 filtfijem ly 17 <+A< hdlq.,?,9/1:', 11/, 71 kq b. Suppose a community has.10 parts per million nox and the average home size is 8 rooms. Please calculate the predicted home price in dollars.. 9, ' ,j2, VS 5; p, cf 2. (1 6 / 1'i, f/.6s tt*yr2e 1. e /3,33 Numbers 37 a r "'7 ~ g 3. a. Please give an example of an unbiased, efficient estimator of a population b. Whd does efficient mean in this context? ' 4 VG/14*tc, c. Please give an example of an unbiased and inefficient estimator of the population mean. d. Please give an example of a biased estimator of the population mean.

5 4. a. What is the Chow test and what idea would I test with it? r.ie c / I ~ ~ ~ ~JJ JCQYMIIPJ LVX~MID PP~,Y~J,.., ('d~ FA(( 4011 cr,r P dl#~j /ul 4 I~J. pplj dhh ~ ~ i,,j ~ p. ~ d,@"j /he ~ d d p ~ " o ~f 'shr ~84 b. If Q= output, K= capital and L= labor, what regression would I run to estimate a CobbDouglass production function? Q /A 6, +4! '4 /+ 5. The data set "cost" has two variables; TC = Total Cost and Q = Quantity. a. Run the regression TC = bl + b2 Q b. What would be a better SIMPLE regression? Please run such a regression and write the answer below. (Hint: Graph the data.) + (,prin 0,,,%lgr.y4 f "<$b@ / 7~.r\I,0'l u4 + 1 ~7 1,~: fl?r?fk n2:clq, 5% i 7C' f L c. Why is the regression in part b better? Explain how you can tell? efif"' aflwfj ( c5 2 3, '/q,,,

6 6. We can use the sample regression as a "good" estimate of the population regression parameters if certain assumptions are made. Cite four and explain each in a sentence. m AC Lic/b. ~drfebih C., 4 0.M, ~vt,/e errurr a rf d~ /I$ g l u, zo hnubui7 / P O &//s WJ A ~h6.w 7. Please go to the cite htt~:// and gather data for the year (Column 1) and level of Real GDP (Column 2) for the period (DO NOT include the quarterly data at the bottom.) a. Paste it into SPSS and run a regression to determine the annual growth rate in real GDP in that time period. Write your regression results below. b. What is the annual percentage growth in GDP over that time period? (Please express answer as a percent.)