I have been using this forum as a reference for multiple classes, it's a great community! I have two questions that I am pretty stumped on.
here is the first:
Suppose that you are interested in estimating the ceteris paribus (all things equal or the same) relationship between y and x1. For this purpose, you can collect data on two control variables, x2 and x3. (For concreteness, you might think of y as nal exam score, x1 as class attendance, x2 as GPA up through the previous semester, and x3 as SAT or ACT score.) Let ~ 1 be the simple regression estimate from y on x1 and let ^ 1 be the multiple regression estimate from y on x1; x2; x3.
(i) If x1is highly correlated with x2 and x3 in the sample, and x2 and x3 have
large partial eects on y, would you expect ~ 1 and ^ 1 to be similar or very
dierent? Explain.
(ii) If x1 is almost uncorrelated with x2 and x3, but x2 and x3 are highly
correlated, will ~ 1 and ^ 1 tend to be similar or very dierent? Explain.
(iii) If x1 is highly correlated with x2 and x3, and x2 and x3 have small partial
eects on y, would you expect se( ~ 1) or se( ^ 1) to be smaller? Explain.
(iv) If x1 is almost uncorrelated with x2 and x3, x2 and x3 have large partial
eects on y, and x2 and x3 are highly correlated, would you expect se( ~ 1)
or se( ^ 1) to be smaller? Explain.
The next one is:
Consider the equation
Y = 0 + 1X1 + 2X2 + u:
From the following data, estimate the regression coecients 0, 1, and 2:
Y = 367:693 X1 = 402:760 X2 = 8:0 n = 15
Σ
(Yi Y )2 = 66042:269
Σ
(X1i X1)2 = 84855:096
Σ
(X2i X2)2 = 280:000
Σ
(Yi Y )(X1i X1) = 74778:346
Σ
(Yi Y )(X2i X2) = 4250:900
Σ
(X1i X1)(X2i X2) = 4796:000
Hint: Recall ~ 1 = ^ 1 + ^ 2^1
I attached a photo of this question as it didn't copy and paste very nicely...
Any help is greatly appreciated. I am also looking for a tutor!
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