Unit 5 ECONF16 (assignment answer key)(1)

# C conduct a four step hypothesis test for the problem

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(c) Conduct a four-step hypothesis test for the problem in textbook question (ii). (“Dropping educ and age from the equation gives …”) p. 162 (F-test) 2

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Step #1 Ho : β educ = 0, β age = 0 Ha : at least one≠ 0 Step #2 This hypothesis test is based on the F- distribution with 2, 702 degrees of freedom. α = 0.05 Reject the Ho if the F-test stat > 3.01 and p- value < 0.05. EXCEL command for the critical value: =F.INV.RT(0.05,2,702) Step #3 Looking at the data for this question (see p. 150): F = ( 0.113 0.103 )/ 2 ( 1 0.113 ) / 702 = 3.957 p-value = 0.020 Note the p-value was found in EXCEL using the command: =F.DIST.RT(3.957,2,702) Step #4 Since 3.958 > 3.01 AND 0.020< 0.05 Reject the Ho. At least one of these coefficients is not equal to 0. 3
#2. For this question you will use the data set: hprice1.dta. Please look at the information in Question C2 [p. 110] and Question C3 [p. 165]. (Both of these textbook questions are based on the data set HPRICE.) Use this information to answer the following questions: (a) Write out the estimated equation for the model shown in C2 [p. 110]. ^ y =− 19.315 + 0.128 ( sqrft ) + 15.198 ( bdrms ) (b) Please answer textbook question (vi) for C2 [p. 110]. Note that you will need information provided in (v). ^ y =− 19.315 + 0.128 ( 2,438 ) + 15.198 ( 4 ) ^ y = 353.541 The predicted house price would be 353,541. As the house actually sold for 300,000 the estimate residual would be -53,541. The underpaid what would have been expected for a house with the square footage and number of bedrooms. Note: if you included more decimal places than I did in your work, your answers may differ somewhat from what I computed here. (c) Please complete textbook questions (i) – (iii) for C3 [p. 165]. Note that you will need to create ln(price) in your data set to complete this question. Textbook questions: (i) After creating the ln(price) you can find the estimated equation: ^ ln ( price )= 4.766 + 0.000379 ( sqrft ) + 0.0289 ( bdrms ) use this to construct ^ θ 1 = 150 ( 0.000379 ) + 0.0289 = 0.0875 . This is the estimated change in price for adding a 150 sqrft bedroom to a house. Thus such an addition would be expected to increase the house price by 8.75%. (ii) Now the goal is to write β 2 in terms of β 1 and θ 1 , this comes from re-arranging the definition given in (i) : β 2 = θ 1 150 β 1 To find the standard error as required by (iii), use this definition to rewrite your population model allowing STATA to directly estimate θ 1 : 4

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ln ( price ) = β 0 + β 1 ( sqrft ) + ( θ 1 150 β 1 ) ( bdrms ) + u Then re-arrange: ln ( price ) = β 0 + β 1 ( sqrft 150 bdrms ) + θ 1 ( bdrms ) + u (iii) To estimate this model in STATA, you must first create a new X-regressor, new = sqrft – 150*bdrms in STATA . generate new = sqrft-150*bdrms and estimate the model: ^ ln ( price )= 4.766 + 0.0875 ( bdrms ) + 0.000379 ( new ) Note that the estimate is the same as found above, 0.0875, but now from STATA you also have a

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