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Midterm ExamECON 3210 O: Use of Economic DataLaura SalisburyYork UniversityFebruary 6, 2014This exam contains 4 questions and 7 pages (including this one), for a total of 60 points.Read questions carefully, and answer all questions in the booklets provided.Formulas andtables are provided on the last three pages of the exam. You may use a calculator. You have90 minutes. Good luck!1
1. For each of the following, indicate whether the statement is true or false.Explain youranswers(a)(4 pts)The least squares estimatorb2is only unbiased if the assumption thatE(e) = 0 holds.(b)(4 pts)When the variance of the error term (σ2) is unknown, the test statisticbk-crˆσ2∑(xi-x)2obeys atdistribution withN-2 degrees of freedom.However, whenσ2is know, the test statisticbk-crσ2∑(xi-x)2obeys atdistribution withNdegrees offreedom.(c)(4 pts)Type II error occurs when you fail to reject a false null hypothesis.(d)(4 pts)You are interested in testingH0:β2= 0 against the alternativeH1:β26= 0,usingα= 0.05.The p-value you obtain for this test is 0.25.Thus, you shouldconclude thatβ2= 0.2. You are interested in estimating the effect of rainfall on umbrella sales. You obtain dataon annual rainfall and umbrella sales from 75 cities in 2013. You estimate the followingregression equation, wherexiis millimetres of rain in 2013 in cityi(in hundreds) andyiis 2013 umbrella sales in cityi(in hundreds):yi=b1+b2xi+eiUse the following information to answer parts (a)-(d):y= 27.9x= 10.0ˆei=-3.9whenxi= 15andyi= 40\var(b1) = 0.0588NXi=1x2i= 15,675.4(a)(4 pts)Calculateb1and interpret its meaning.(b)(4 pts)Calculateb2and interpret its meaning.