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Unformatted text preview: 18062386 Econ 140 Problem Set # 2 [4.12] [A.] H o : Beta 3 = Beta 5 = H a : Beta 3 Beta ≠ 5 ≠ F C = [(ESS R- ESS U ) /(DF R-DF m )] /(ESS U /DF U )] F C = ((44.659-23.51)/2)/(23.51/(40-5)) = 15.742 [B.] F(k-m, n-k) = F(2,35); df R =37, df U =35 [C.] F* is between 5.39 and 5.18 for F (2, 35) at the 1% significance level. If F C > F*, we reject the null hypothesis (H o ) because Beta 3 and Beta 5 are jointly significant since P(F C >F*) = 0. [D.] n-k = d.f. = 39 [E.] T* is between 1.684 and 1.697 [F.] T c T cn = ( B cn-0)/s cn if greater than T* then significant If T Ck > T* Beta K is statistically significant a. T c1 = 0.54892 < 1.684 statistically insignificant b. T c2 = 2.0556 > 1.697 statistically significant c. T c3 = 1.7918 > 1.697 statistically significant d. T c4 = 3.1246 > 1.697 statistically significant e. T c5 = 0.24329 < 1.684 statistically insignificant [G.] Based on the F-test performed in part (f), variable B 5 should be omitted from the model. The reason for doing so is because this variable is statistically insignificant at the 10% level and the advantages of removing the variable will mean that you need to obtain less information and test less variables (which will also increase the d.f. of your test as well) since testing B 5 will not add much to your test. However, omitting a variable like this or another variable may be a disadvantage because the variable might actually be significant and the results were simply because the sample was poorly administered. In addition, omitting the constant variable may lead to bias in the estimated variables. [ H.] INCOME* = 1000(INCOME) 1. INCOME = INCOME* /1000 2. B INCOME = 0.003159/1000= 0.000003159 * INCOME 3. 0.001763/1000 = 0.000001763 = SE(INCOME) [I.] CONSTANT: I would expect this coefficient to be positive, because if all other variables were zero, then I would expect there to still be some demand for cars (however unaffordable) However, the coefficient is in fact negative and this would be that there would be negative sales of cars if there were no other variables to consider. I would instead expect it to be either slightly positive or 0. PRICE: This variable measures how the demand for the number of cars changes as the price of the car changes. We would expect the sign on this coefficient to be negative, which it is because the law of demand dictates that as price of a good increases, the quantity demand decreases generally. INCOME: Since this coefficient measures the relationship with income on quantity of cars demanded, we would expect this coefficient to be positive because of the income effect. The coefficient is as is expected. As people have more money to spend, the number of cars demanded increases....
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- Spring '08