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practiceFinalSolutions07

practiceFinalSolutions07 - AW‘SLQGLX‘ Econ 334 Practice...

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Unformatted text preview: AW‘SLQGLX‘ Econ 334: Practice Final Exam 7 1. Of the four assumptions for simple linear regression, which is most directly connected with estimating the slope coefficient? EDA Klzo 2. Suppose you run a regression of student’s final exam scores on their previous previous grades: f incl,- = [30 + filmidtermlg + ,BzmidtermZg + 'u..; (a) How many points more would we expect you to do on the final if you had scored 5 more points on midterm2? 5131 (b) Now suppose that students with lower midterm grades studied harder for the final. What does this do to our prediction of your final grade? Is it too high or too low? Be specific about what is correlated with what. EXpch MKALW‘E “1% Le, ”Pesfl-{w-lj carve/(WM 4 Anal 3 Vanda. £qu Wat'l‘luainf cave/QM 63/ “KM dipoirf HA (Lea. lurker 49.4w,“ , TIM/g we, Lkpad’ 0L MAHUL [Amman/vol. LCOLS 7n 1 , B1 er 3. You run a complex model to determine if cigarette prices (cigprice) determine mum of cigarettes smoked per day (cigs). white is a dummy variable which is one if the person is white. Call: lm(formula - cigs ” logIncome + age + ageSq + cigprice + educ + white + white * educ, data = smoke) Residuals : Min 10 Median 3Q Max -15.038 -9.149 -6.704 8.093 71.017 Coefficients: Estimate Std. Error t value Pr(>|tl) (Intercept) -0.647517 10.839155 -0.060 0.952 logIncome 0.676953 0.761178 0.889 0.374 age 0.734925 0.167618 4.385 1.33e—05 *** ageSq -0.008627 0.001816 —4.751 2.43e—06 *** cigprice —0 035384 0.106931 -0.331 0.741 educ —0.650954 0.443422 -1 468 0.143 white -2 432749 6.094492 —0.399 0.690 educzwhite 0.183638 0.473142 0.388 0.698 Residual standard error: 13.56 on 748 degrees of freedom Multiple R-Squared: 0.04161,Adjusted R-squared: 0.03264 F-statistic: 4.639 on 7 and 748 DF, p-value: 4.246e-05 1 (a) How many more or less cigarettes does a person smoke if they’re White? ZH-fiwM* (b) How many more or less cigarettes does 40—year-old smoke compared to a 39-year “d" 043‘; - 0. 008% 402—392) (c) How many more or less cigarettes does a white person with 10 years of education smoke compared with a white person with 9\years of education? ,-:i;=~~r » ,\ \ K ' = \— 7/ —O.(o‘>l + o. l%& , o , ‘ I (d) Why did we include ageSq in the regression? What effect does it capture? Wan/chm a? Qaibjcfi ‘- \l‘w Law [Auto-A37. (e) Interpret the coefficient on logIncome. How does cigs change with income? As imam/mo. iimmases, ALL LLfi-L LILUL (Miami, MUMPHW of; c'gmjfii‘es \“Wmsas. 4. ,31 in some regression is 3. Its standard error is estimated to be 1. (a) Is this enough information to conclude that the variable is stastically significant? Write down the null and alternative hypotheses you’re testing. \ieS'. Re" 1350 Ml: IN #0 (b) Create 95% confidence intervals for [31. (Use a rule of thumb for the math.) 3126 = [UK] (c) Do we know enough to conclude if the variable is economically significant? What else would we need to know? poi/dd th‘d's X'xl Me, Measured]. in , voLLPLe/r +9,» Vax‘mloLas Lune ism ‘stcermdl ) 05k. 5. In the regression wage = ,60 + ,Blage + figage2 + [33educatz'on + u: (a) How can you test if education is a significant variable? Specify the type of test you’d run and write out null and alternative hypotheses. gt-W “0113,30 HI“. 123-190 (b) How can you test that education is the only significant variable? Specify the type of test you’d run and write out null and alternative hypotheses. F'l‘ag‘h DY- LM'it—S‘l— Ho Ef‘Fz'tO, ’H‘: ‘3‘=fo bf fi-fif D 6. You have data on wage, age, education, and firstJob (a dummy variable which is 1 if a person is on their first full-time job). (a) Write down a regression model that allows for people’s first-time jobs to pay less, all other things held equal. £00439. : ¥°4?\—&mtTok+ 1,10%; 4» 'Fgecfl 40L (b) Write down a regression model that allows for first-time jobs to pay more for additional education. way: 130 "‘3 QMJCSJO + 15103. + ”’33 ibivsgolokwfl i F1 0% “L“ 7. You run the regression model y = 50 + film + u and find out that u has a variance that’s proportional to 2:. (a) What is this condition called? hie/WOSMAS‘HCCW (b) What are the consequences of this condition for 51? Be specific about bias and testing (or confidence intervals). (g‘ '1: S'ELL \Mloia [gmt 1’84; LmCich/lm micwols mlu Lie 4-90 um , Gag. ‘l-QS'iS will Ye] Qti‘ 4&9. Whit? 14 “a“ 7‘ (c) Write down a transformed model which doesn’t suffer from this condition. L6.— .._+\L lA “AMI-B fi_rfibfi¥fi+ (lamb. Pia.» (d) In three sentences (or equations), describe how you’d test for this condition using the residuals from the above regression. B_? 115%.. Squaw ‘l'Q—L realMS, ire-TASS ‘l‘eau’v M X, ?ouao,rg D'Q’ K, 1? were. SiauiQLcm/ci cauaiucflk We. Micros Mag-(1:111 8. You’re building a model of the 2008 election based on how people voted in the past and their income. (There are two parties, “Elephant” and “Donkey”.) Consider the linear probability model: y = prob(voteDm1key2003) = [30 + filvotedDmkeygoM + flgincome + u. (a) A big problem with the linear probability model is that, as the probability gets nearer 0 or 1, its variance decreases. What is the name of this problem? new SWSH Ll M!) (b) If you’re making a binary choice (like “elephant” or “donkey”), the variance of the probability of choosing one or the other is var (prob(z)) = prob(z) (1 — prob(z)). How could you solve the problem you named? Write down a transformed equa- tion which doesn’t suffer from the flaw above (Hint: you can use an estimated value to make the math simpler.) 30 wt (kwouo lat x\- 1% L L — %\ g, :- - . . L‘bt‘. - :5 %(1—%\ 9. You’re interested in the Phillips curve. You have time-series data for both inflation and unemployment. (a) Write down a model that allows you to estimate the percent change in inflation which arises from a. percent change in unemployment. fingc‘lwumfimw 3 ’Fo + F [63( MLDVW"\ + UL (b) If you think that the relationship between inflation and unemployment was signif— icantly different during the 1970’s, what variable would you add to the regression? How would you test this? dz“) (3 a. CLUWLu/u/ Va-«rioucaLL (‘0‘ ids (CT-RB flogfimélaliab= “(3° a]; Olga—112,1 [03CUMPLik’wd\+ szgci £§(:MP\ (c) Now 1magine that you discover that unemployment 1s highly serially correlated in your monthly data. Write down in math what this means. \AAwwxs w) ‘fiw wfi'kfl/VLUL U‘MUMFioklmi/uti IS Cowelmétca ”OLA“ UWofiMLQA/Lfi- 1 (d) Is the serial correlation 1n unemployment necessarily a problem for your regres- sion? Not WSWLLV- jig MLYSJLM Syria-L Watt/Chm in (e) Now suppose you find serial correlation in your residuals. Is this a problem for Yes. “6M3 oor (F's WILL ice, fo‘camcfl. the regression? 10. You find serial correlation in the regression residuals of your favorite time-series re- gression! (y; = Bo + 16113 + 10:) (a) What are the consequences for the coefficient of interest, fil? Be specific about bias and hypothesis testing. SUV £S~decfi A unik lop. uwkaiocbecg) Lei couccflwu‘ 1 \WL-‘exwaLg coKLK +30 Swoik moQ wa‘kL [0.2, New; \‘twfi ”\‘0 (”DmiSeLtB rapt? +0“— VWLL \A‘IP06’L’ZSIS (b) You fit an AR(1) model to the residuals: at = put_1 and find fh/o = 0.5. Write down a transformed model which does not suffer from serial correlation in the errors. %x*0-5‘ar~t = (Po +"F. (Xx —o.‘5 km} 4 (LI (c) Suppose I insisted that you didn’t have serial correlation in your errors. Propose a simple test to prove me wrong. Write down the null and alternative h otheses. J: H‘o .' A z: 0 (RP-fines residamds m lowland. vesiwfi } b‘i‘BofFa .‘ 4 C H . =|rl 11. Write down the steps for conductlng a functional-form misspec1fication test of your " T" O choosing. Rm @3512 find -§iafi,g V‘CgHSSli/L 32‘P°+F,K {-LL . 9’1 r M .3 HAM NSVLSS a: “Joba 4’ (X28 +6 M M [F-Fasi\ Ho'- «909:0 Hg oméo Ur «Ho 12. You’re interested in modeling the elasticity of ice cream sales to price. However, you notice a large seasonal component in the quantity of ice cream consumed which you’d like to account for in order to refine your elasticity estimate. (a) Write down a model which relates the percent change in ice cream consumed to a percent change in its price, accounting for seasonal effects. Describe any variables besides icecream and price that you choose to include in your model. floataX : “120 't “F leaqwlmk + $2 w‘wnjcev +F3 Spvifi + Pal Squlqupt/K WW midday, flpv‘rus, SUI/1AM M 6001441447 vow “Ling (b) I claim that the seasonal patterns don’t matter. Propose a test (be specific about null, alternative, and test type) to prove me wrong. uo--W>~L=a=7>«=~° 2*" ”FL?“ ”3*“ "MO "resi \Dl 9&ij av LWL +asi (c) Now suppose you think that ice cream consumption has been increasing over time for non-price reasons. Add something to your seasonal model in part (a) which allows for estimation of non-price annual growth in ice cream consumption. [08 Cu”:— $°+F lESL—fvtu.\-t 'F1, Unwicv —( F5 SFvws-di ’F‘l SUM/MW Egfl W "t LL ‘ 13. In class we estimated the+ response of crime rates (crime) to additional spending on police forces (cops) using a cross-section of US cities, and found (surprisingly) that spending more on police was correlated with more crime! (a) Why did this happen? What was missing in the above regression? Explain this carefully (what needs to be correlated with what?). Is WWW! lo! a Cops was MW03~ 1+ (£9me 15—“ inputs DQ C/‘THIUL‘L What—tor wows missuxa was SM wsurf. DC Truloos CXI‘IMQ mast-‘28 (b) Suppmmmmmmmmfifiu’mmflnstead ofjusttheone). What’stheaimplestwaytoreaolvethepmblemin(a)? 'C‘LQ S "LII/Hind; lMSk (:1er (Lacta~ (aflgufl aQn‘TchaMt 11am Cami; Tic—Ff; COPS: VFLC/rlmqvfi— (Lt (c) Now suppose we had a two—year panel dataset with both crime rates and expenses for each city. Write down the equation (or describe the procedure) that you would use to estimate the effect of increased police spending on crime rates. COM Jutoux dQQCuu/Lcn err Sulatmd' 04 +¢m Series away CWWLUth-g CrlMQiifl—Z "Best? (besii —— COPS). i1» +LL [CHM/ntli— Chm)» = 'Fo 4r Tn CCOnguc— COFSL +Lg 14. A pooled cross-section is made of two or more random samples taken at different times, often with dummyvariables for the time that the sample is taken. A panel dataset is similar but follows individual units over time. (a) What, does the panel dataset allow us to estimate that the pooled cross-section does not? F3)“; “aw-(S 7 W mAMA-wdl SPQCl'QlC ‘bm SQJHQS \‘M'Q’VCQflS (b) What old problem does this allow us to solve if we make the additional assump- tion that something 1s constant over time? And how? EJ; M W\‘\' thvqw \féaLwawcl’ ’VMlal’ong, Lat V‘L comm-l MRS ‘l-ww. ‘lbr WA (flux/14ml we owe. wove «LL; +0 6,li 190v we (c) How would you remove the fixed effects from the panel data so that you could then use plain old least-squares regression techniques? 1:614" SuLMc’l VLL ‘FlWJz-SD.2¢‘\(L<5 M—é’w—aflflg % Wt, \«Mmcflcwt Wisdohzs. 15. You’re interested in t e hypothesis that the Reagan-era tax cuts spurred GDP growth. You have data on GDPt. (a) Write a regression equation that allows you to test the hypothesis that the GDP growth rate (the annual percent change in GDP) changed after 1984. Describe any additional variables you bring to the regression. fl. (GDP): 0+ {Aqufl‘imsr 24km. +Lu 08 ' (F ”F [(6 «pin/K (in: is a ' «Io/violin b What kind of test would on use? S ecifi test e, null, and alternative h - ( ) y p y typ y few $°3{‘%% potheses. i-M: “(333,250 H.%$,%O 16. You fit the model y = ,30 +fi131 + flgzz + @3223 + u. You have 32 observations for each , variable. Below, describe the tests requested, being specific about test types, null and alternative hypotheses, test statistics, and critical values you’d look up. (a) Test if 22 is statistically significant. 3% O . . 2. — seem Rig-F50 “5‘ 35° is“ . fig (LBHULL Valium: 7t (13’ O qttra‘) 1 (b) Test if any of the m’s are statistically significanl. 3‘“st ‘- “o‘- $\=%z:%3:0 an: $14”) 5»?;,_:é0 Or?5¥o (c)1:estifé=\12. N ‘ F' Slat“ 33%"SSR‘M 28’ O _,_.——— 9" ll \ SSR l)» 3 Jg’mt— ‘ Cvlfical whim *9: $50,, _ r mV£7fifl, BOISE R I" (\Z l "1’: l2 \ i'Stazt‘. é, - l 2 Critical value? ~ \, \ a? 3E [’28, e.q1}5§ ...
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