# midterm_2017.pdf - Name Columbia UNI Midterm Exam Fall 2017...

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Name. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Columbia UNI. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Midterm Exam Fall 2017Linear Regression ModelsGroup DOctober 20, 2017
Problem 1 (20p)(i) (10p) LetY1, . . . , YNbe independent observations drawn from a population with unknown fi-nite meanθ. Show that the sample meanbθ=1NNi=1Yiis an unbiased estimator ofθ.
(ii) (10p) Find the variance of the sample mean estimator from (i) above.
2
Problem 2 (40p)A student in a university polledN= 10 colleagues about the number of classesXof theLinear Regression course which they attended in the past semester and the scoreYwhichthese students got on the final exam for this course.In order to keep the information about the lecture attendance and exam performanceof her colleagues private, she reported only the following summary statistics:NXi=1X2i= 1559,NXi=1XiYi= 7994,NXi=1Xi= 95,andNXi=1Yi= 584,Your task is to(i)(5p) find the estimates of the coefficients of the simple linear regression model for this data,