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Introductory Econometrics 4th Edition by Jeffrey Wooldridge
Edition 4ISBN: 978-0324660609Introductory Econometrics 4th Edition by Jeffrey Wooldridge
Edition 4ISBN: 978-0324660609 Exercise 6
Let ![Let 0 and 1 be the intercept and slope from the regression of y i on x i , using n observations. Let c 1 and c 2 , with c 2 0, be constants. Let 0 and 1 be the intercept and slope from the regression of c 1 y i on c 2 x i. Show that 1 = (c 1 /c 2 ) 0 and 0 = c 1 0 , thereby verifying the claims on units of measurement in Section 2.4. [Hint: To obtain 1 , plug the scaled versions of x and y into (2.19). Then, use (2.17) for 0 , being sure to plug in the scaled x and y and the correct slope.] (ii) Now, let 0 and 1 be from the regression of (c 1 + y i ) on (c 2 + x i ) (with no restriction on c 1 or c 2 ). Show that l = 1 and 0 = 0 + c 1 - c 2 1. (iii) Now, let 0 and 1 be the OLS estimates from the regression log(y i ) on x i , where we must assume y i. 0 for all i. For c 1 0, let 0 and 1 be the intercept and slope from the regression of log(c 1 y i ) on x i. Show that . (iv) Now, assuming that x. 0 for all i, let 0 and 1 be the intercept and slope from the regression of y. on log(c 2 x i ). How do 0 and 1 compare with the intercept and slope from the regression of y i on log(x i )](https://storage.examlex.com/SM2712/11eb9ee2_f06c_032f_8edd_27ac049cc120_SM2712_11.jpg)
0 and ![Let 0 and 1 be the intercept and slope from the regression of y i on x i , using n observations. Let c 1 and c 2 , with c 2 0, be constants. Let 0 and 1 be the intercept and slope from the regression of c 1 y i on c 2 x i. Show that 1 = (c 1 /c 2 ) 0 and 0 = c 1 0 , thereby verifying the claims on units of measurement in Section 2.4. [Hint: To obtain 1 , plug the scaled versions of x and y into (2.19). Then, use (2.17) for 0 , being sure to plug in the scaled x and y and the correct slope.] (ii) Now, let 0 and 1 be from the regression of (c 1 + y i ) on (c 2 + x i ) (with no restriction on c 1 or c 2 ). Show that l = 1 and 0 = 0 + c 1 - c 2 1. (iii) Now, let 0 and 1 be the OLS estimates from the regression log(y i ) on x i , where we must assume y i. 0 for all i. For c 1 0, let 0 and 1 be the intercept and slope from the regression of log(c 1 y i ) on x i. Show that . (iv) Now, assuming that x. 0 for all i, let 0 and 1 be the intercept and slope from the regression of y. on log(c 2 x i ). How do 0 and 1 compare with the intercept and slope from the regression of y i on log(x i )](https://storage.examlex.com/SM2712/11eb9ee2_f06c_0330_8edd_396e33626c5e_SM2712_11.jpg)
1 be the intercept and slope from the regression of y i on x i , using n observations. Let c 1 and c 2 , with c 2 0, be constants. Let ![Let 0 and 1 be the intercept and slope from the regression of y i on x i , using n observations. Let c 1 and c 2 , with c 2 0, be constants. Let 0 and 1 be the intercept and slope from the regression of c 1 y i on c 2 x i. Show that 1 = (c 1 /c 2 ) 0 and 0 = c 1 0 , thereby verifying the claims on units of measurement in Section 2.4. [Hint: To obtain 1 , plug the scaled versions of x and y into (2.19). Then, use (2.17) for 0 , being sure to plug in the scaled x and y and the correct slope.] (ii) Now, let 0 and 1 be from the regression of (c 1 + y i ) on (c 2 + x i ) (with no restriction on c 1 or c 2 ). Show that l = 1 and 0 = 0 + c 1 - c 2 1. (iii) Now, let 0 and 1 be the OLS estimates from the regression log(y i ) on x i , where we must assume y i. 0 for all i. For c 1 0, let 0 and 1 be the intercept and slope from the regression of log(c 1 y i ) on x i. Show that . (iv) Now, assuming that x. 0 for all i, let 0 and 1 be the intercept and slope from the regression of y. on log(c 2 x i ). How do 0 and 1 compare with the intercept and slope from the regression of y i on log(x i )](https://storage.examlex.com/SM2712/11eb9ee2_f06c_0331_8edd_9f3534e1a070_SM2712_11.jpg)
0 and ![Let 0 and 1 be the intercept and slope from the regression of y i on x i , using n observations. Let c 1 and c 2 , with c 2 0, be constants. Let 0 and 1 be the intercept and slope from the regression of c 1 y i on c 2 x i. Show that 1 = (c 1 /c 2 ) 0 and 0 = c 1 0 , thereby verifying the claims on units of measurement in Section 2.4. [Hint: To obtain 1 , plug the scaled versions of x and y into (2.19). Then, use (2.17) for 0 , being sure to plug in the scaled x and y and the correct slope.] (ii) Now, let 0 and 1 be from the regression of (c 1 + y i ) on (c 2 + x i ) (with no restriction on c 1 or c 2 ). Show that l = 1 and 0 = 0 + c 1 - c 2 1. (iii) Now, let 0 and 1 be the OLS estimates from the regression log(y i ) on x i , where we must assume y i. 0 for all i. For c 1 0, let 0 and 1 be the intercept and slope from the regression of log(c 1 y i ) on x i. Show that . (iv) Now, assuming that x. 0 for all i, let 0 and 1 be the intercept and slope from the regression of y. on log(c 2 x i ). How do 0 and 1 compare with the intercept and slope from the regression of y i on log(x i )](https://storage.examlex.com/SM2712/11eb9ee2_f06c_0332_8edd_9d2937f18b23_SM2712_11.jpg)
1 be the intercept and slope from the regression of c 1 y i on c 2 x i. Show that ![Let 0 and 1 be the intercept and slope from the regression of y i on x i , using n observations. Let c 1 and c 2 , with c 2 0, be constants. Let 0 and 1 be the intercept and slope from the regression of c 1 y i on c 2 x i. Show that 1 = (c 1 /c 2 ) 0 and 0 = c 1 0 , thereby verifying the claims on units of measurement in Section 2.4. [Hint: To obtain 1 , plug the scaled versions of x and y into (2.19). Then, use (2.17) for 0 , being sure to plug in the scaled x and y and the correct slope.] (ii) Now, let 0 and 1 be from the regression of (c 1 + y i ) on (c 2 + x i ) (with no restriction on c 1 or c 2 ). Show that l = 1 and 0 = 0 + c 1 - c 2 1. (iii) Now, let 0 and 1 be the OLS estimates from the regression log(y i ) on x i , where we must assume y i. 0 for all i. For c 1 0, let 0 and 1 be the intercept and slope from the regression of log(c 1 y i ) on x i. Show that . (iv) Now, assuming that x. 0 for all i, let 0 and 1 be the intercept and slope from the regression of y. on log(c 2 x i ). How do 0 and 1 compare with the intercept and slope from the regression of y i on log(x i )](https://storage.examlex.com/SM2712/11eb9ee2_f06c_0333_8edd_7b444cddb4fc_SM2712_11.jpg)
1 = (c 1 /c 2 ) ![Let 0 and 1 be the intercept and slope from the regression of y i on x i , using n observations. Let c 1 and c 2 , with c 2 0, be constants. Let 0 and 1 be the intercept and slope from the regression of c 1 y i on c 2 x i. Show that 1 = (c 1 /c 2 ) 0 and 0 = c 1 0 , thereby verifying the claims on units of measurement in Section 2.4. [Hint: To obtain 1 , plug the scaled versions of x and y into (2.19). Then, use (2.17) for 0 , being sure to plug in the scaled x and y and the correct slope.] (ii) Now, let 0 and 1 be from the regression of (c 1 + y i ) on (c 2 + x i ) (with no restriction on c 1 or c 2 ). Show that l = 1 and 0 = 0 + c 1 - c 2 1. (iii) Now, let 0 and 1 be the OLS estimates from the regression log(y i ) on x i , where we must assume y i. 0 for all i. For c 1 0, let 0 and 1 be the intercept and slope from the regression of log(c 1 y i ) on x i. Show that . (iv) Now, assuming that x. 0 for all i, let 0 and 1 be the intercept and slope from the regression of y. on log(c 2 x i ). How do 0 and 1 compare with the intercept and slope from the regression of y i on log(x i )](https://storage.examlex.com/SM2712/11eb9ee2_f06c_0334_8edd_d508b327fe6d_SM2712_11.jpg)
0 and ![Let 0 and 1 be the intercept and slope from the regression of y i on x i , using n observations. Let c 1 and c 2 , with c 2 0, be constants. Let 0 and 1 be the intercept and slope from the regression of c 1 y i on c 2 x i. Show that 1 = (c 1 /c 2 ) 0 and 0 = c 1 0 , thereby verifying the claims on units of measurement in Section 2.4. [Hint: To obtain 1 , plug the scaled versions of x and y into (2.19). Then, use (2.17) for 0 , being sure to plug in the scaled x and y and the correct slope.] (ii) Now, let 0 and 1 be from the regression of (c 1 + y i ) on (c 2 + x i ) (with no restriction on c 1 or c 2 ). Show that l = 1 and 0 = 0 + c 1 - c 2 1. (iii) Now, let 0 and 1 be the OLS estimates from the regression log(y i ) on x i , where we must assume y i. 0 for all i. For c 1 0, let 0 and 1 be the intercept and slope from the regression of log(c 1 y i ) on x i. Show that . (iv) Now, assuming that x. 0 for all i, let 0 and 1 be the intercept and slope from the regression of y. on log(c 2 x i ). How do 0 and 1 compare with the intercept and slope from the regression of y i on log(x i )](https://storage.examlex.com/SM2712/11eb9ee2_f06c_2a45_8edd_9d12298744be_SM2712_11.jpg)
0 = c 1 ![Let 0 and 1 be the intercept and slope from the regression of y i on x i , using n observations. Let c 1 and c 2 , with c 2 0, be constants. Let 0 and 1 be the intercept and slope from the regression of c 1 y i on c 2 x i. Show that 1 = (c 1 /c 2 ) 0 and 0 = c 1 0 , thereby verifying the claims on units of measurement in Section 2.4. [Hint: To obtain 1 , plug the scaled versions of x and y into (2.19). Then, use (2.17) for 0 , being sure to plug in the scaled x and y and the correct slope.] (ii) Now, let 0 and 1 be from the regression of (c 1 + y i ) on (c 2 + x i ) (with no restriction on c 1 or c 2 ). Show that l = 1 and 0 = 0 + c 1 - c 2 1. (iii) Now, let 0 and 1 be the OLS estimates from the regression log(y i ) on x i , where we must assume y i. 0 for all i. For c 1 0, let 0 and 1 be the intercept and slope from the regression of log(c 1 y i ) on x i. Show that . (iv) Now, assuming that x. 0 for all i, let 0 and 1 be the intercept and slope from the regression of y. on log(c 2 x i ). How do 0 and 1 compare with the intercept and slope from the regression of y i on log(x i )](https://storage.examlex.com/SM2712/11eb9ee2_f06c_2a46_8edd_6f508eac399f_SM2712_11.jpg)
0 , thereby verifying the claims on units of measurement in Section 2.4. [Hint: To obtain ![Let 0 and 1 be the intercept and slope from the regression of y i on x i , using n observations. Let c 1 and c 2 , with c 2 0, be constants. Let 0 and 1 be the intercept and slope from the regression of c 1 y i on c 2 x i. Show that 1 = (c 1 /c 2 ) 0 and 0 = c 1 0 , thereby verifying the claims on units of measurement in Section 2.4. [Hint: To obtain 1 , plug the scaled versions of x and y into (2.19). Then, use (2.17) for 0 , being sure to plug in the scaled x and y and the correct slope.] (ii) Now, let 0 and 1 be from the regression of (c 1 + y i ) on (c 2 + x i ) (with no restriction on c 1 or c 2 ). Show that l = 1 and 0 = 0 + c 1 - c 2 1. (iii) Now, let 0 and 1 be the OLS estimates from the regression log(y i ) on x i , where we must assume y i. 0 for all i. For c 1 0, let 0 and 1 be the intercept and slope from the regression of log(c 1 y i ) on x i. Show that . (iv) Now, assuming that x. 0 for all i, let 0 and 1 be the intercept and slope from the regression of y. on log(c 2 x i ). How do 0 and 1 compare with the intercept and slope from the regression of y i on log(x i )](https://storage.examlex.com/SM2712/11eb9ee2_f06c_2a47_8edd_23be39e7e457_SM2712_11.jpg)
1 , plug the scaled versions of x and y into (2.19). Then, use (2.17) for ![Let 0 and 1 be the intercept and slope from the regression of y i on x i , using n observations. Let c 1 and c 2 , with c 2 0, be constants. Let 0 and 1 be the intercept and slope from the regression of c 1 y i on c 2 x i. Show that 1 = (c 1 /c 2 ) 0 and 0 = c 1 0 , thereby verifying the claims on units of measurement in Section 2.4. [Hint: To obtain 1 , plug the scaled versions of x and y into (2.19). Then, use (2.17) for 0 , being sure to plug in the scaled x and y and the correct slope.] (ii) Now, let 0 and 1 be from the regression of (c 1 + y i ) on (c 2 + x i ) (with no restriction on c 1 or c 2 ). Show that l = 1 and 0 = 0 + c 1 - c 2 1. (iii) Now, let 0 and 1 be the OLS estimates from the regression log(y i ) on x i , where we must assume y i. 0 for all i. For c 1 0, let 0 and 1 be the intercept and slope from the regression of log(c 1 y i ) on x i. Show that . (iv) Now, assuming that x. 0 for all i, let 0 and 1 be the intercept and slope from the regression of y. on log(c 2 x i ). How do 0 and 1 compare with the intercept and slope from the regression of y i on log(x i )](https://storage.examlex.com/SM2712/11eb9ee2_f06c_2a48_8edd_d35bb2feb48c_SM2712_11.jpg)
0 , being sure to plug in the scaled x and y and the correct slope.]
(ii) Now, let![Let 0 and 1 be the intercept and slope from the regression of y i on x i , using n observations. Let c 1 and c 2 , with c 2 0, be constants. Let 0 and 1 be the intercept and slope from the regression of c 1 y i on c 2 x i. Show that 1 = (c 1 /c 2 ) 0 and 0 = c 1 0 , thereby verifying the claims on units of measurement in Section 2.4. [Hint: To obtain 1 , plug the scaled versions of x and y into (2.19). Then, use (2.17) for 0 , being sure to plug in the scaled x and y and the correct slope.] (ii) Now, let 0 and 1 be from the regression of (c 1 + y i ) on (c 2 + x i ) (with no restriction on c 1 or c 2 ). Show that l = 1 and 0 = 0 + c 1 - c 2 1. (iii) Now, let 0 and 1 be the OLS estimates from the regression log(y i ) on x i , where we must assume y i. 0 for all i. For c 1 0, let 0 and 1 be the intercept and slope from the regression of log(c 1 y i ) on x i. Show that . (iv) Now, assuming that x. 0 for all i, let 0 and 1 be the intercept and slope from the regression of y. on log(c 2 x i ). How do 0 and 1 compare with the intercept and slope from the regression of y i on log(x i )](https://storage.examlex.com/SM2712/11eb9ee2_f06c_2a49_8edd_f3b8b88dd697_SM2712_11.jpg)
0 and ![Let 0 and 1 be the intercept and slope from the regression of y i on x i , using n observations. Let c 1 and c 2 , with c 2 0, be constants. Let 0 and 1 be the intercept and slope from the regression of c 1 y i on c 2 x i. Show that 1 = (c 1 /c 2 ) 0 and 0 = c 1 0 , thereby verifying the claims on units of measurement in Section 2.4. [Hint: To obtain 1 , plug the scaled versions of x and y into (2.19). Then, use (2.17) for 0 , being sure to plug in the scaled x and y and the correct slope.] (ii) Now, let 0 and 1 be from the regression of (c 1 + y i ) on (c 2 + x i ) (with no restriction on c 1 or c 2 ). Show that l = 1 and 0 = 0 + c 1 - c 2 1. (iii) Now, let 0 and 1 be the OLS estimates from the regression log(y i ) on x i , where we must assume y i. 0 for all i. For c 1 0, let 0 and 1 be the intercept and slope from the regression of log(c 1 y i ) on x i. Show that . (iv) Now, assuming that x. 0 for all i, let 0 and 1 be the intercept and slope from the regression of y. on log(c 2 x i ). How do 0 and 1 compare with the intercept and slope from the regression of y i on log(x i )](https://storage.examlex.com/SM2712/11eb9ee2_f06c_2a4a_8edd_b79a1988e495_SM2712_11.jpg)
1 be from the regression of (c 1 + y i ) on (c 2 + x i ) (with no restriction on c 1 or c 2 ). Show that ![Let 0 and 1 be the intercept and slope from the regression of y i on x i , using n observations. Let c 1 and c 2 , with c 2 0, be constants. Let 0 and 1 be the intercept and slope from the regression of c 1 y i on c 2 x i. Show that 1 = (c 1 /c 2 ) 0 and 0 = c 1 0 , thereby verifying the claims on units of measurement in Section 2.4. [Hint: To obtain 1 , plug the scaled versions of x and y into (2.19). Then, use (2.17) for 0 , being sure to plug in the scaled x and y and the correct slope.] (ii) Now, let 0 and 1 be from the regression of (c 1 + y i ) on (c 2 + x i ) (with no restriction on c 1 or c 2 ). Show that l = 1 and 0 = 0 + c 1 - c 2 1. (iii) Now, let 0 and 1 be the OLS estimates from the regression log(y i ) on x i , where we must assume y i. 0 for all i. For c 1 0, let 0 and 1 be the intercept and slope from the regression of log(c 1 y i ) on x i. Show that . (iv) Now, assuming that x. 0 for all i, let 0 and 1 be the intercept and slope from the regression of y. on log(c 2 x i ). How do 0 and 1 compare with the intercept and slope from the regression of y i on log(x i )](https://storage.examlex.com/SM2712/11eb9ee2_f06c_515b_8edd_db6fbfa1d847_SM2712_11.jpg)
l = ![Let 0 and 1 be the intercept and slope from the regression of y i on x i , using n observations. Let c 1 and c 2 , with c 2 0, be constants. Let 0 and 1 be the intercept and slope from the regression of c 1 y i on c 2 x i. Show that 1 = (c 1 /c 2 ) 0 and 0 = c 1 0 , thereby verifying the claims on units of measurement in Section 2.4. [Hint: To obtain 1 , plug the scaled versions of x and y into (2.19). Then, use (2.17) for 0 , being sure to plug in the scaled x and y and the correct slope.] (ii) Now, let 0 and 1 be from the regression of (c 1 + y i ) on (c 2 + x i ) (with no restriction on c 1 or c 2 ). Show that l = 1 and 0 = 0 + c 1 - c 2 1. (iii) Now, let 0 and 1 be the OLS estimates from the regression log(y i ) on x i , where we must assume y i. 0 for all i. For c 1 0, let 0 and 1 be the intercept and slope from the regression of log(c 1 y i ) on x i. Show that . (iv) Now, assuming that x. 0 for all i, let 0 and 1 be the intercept and slope from the regression of y. on log(c 2 x i ). How do 0 and 1 compare with the intercept and slope from the regression of y i on log(x i )](https://storage.examlex.com/SM2712/11eb9ee2_f06c_515c_8edd_33a8d55038aa_SM2712_11.jpg)
1 and ![Let 0 and 1 be the intercept and slope from the regression of y i on x i , using n observations. Let c 1 and c 2 , with c 2 0, be constants. Let 0 and 1 be the intercept and slope from the regression of c 1 y i on c 2 x i. Show that 1 = (c 1 /c 2 ) 0 and 0 = c 1 0 , thereby verifying the claims on units of measurement in Section 2.4. [Hint: To obtain 1 , plug the scaled versions of x and y into (2.19). Then, use (2.17) for 0 , being sure to plug in the scaled x and y and the correct slope.] (ii) Now, let 0 and 1 be from the regression of (c 1 + y i ) on (c 2 + x i ) (with no restriction on c 1 or c 2 ). Show that l = 1 and 0 = 0 + c 1 - c 2 1. (iii) Now, let 0 and 1 be the OLS estimates from the regression log(y i ) on x i , where we must assume y i. 0 for all i. For c 1 0, let 0 and 1 be the intercept and slope from the regression of log(c 1 y i ) on x i. Show that . (iv) Now, assuming that x. 0 for all i, let 0 and 1 be the intercept and slope from the regression of y. on log(c 2 x i ). How do 0 and 1 compare with the intercept and slope from the regression of y i on log(x i )](https://storage.examlex.com/SM2712/11eb9ee2_f06c_515d_8edd_7b0ac937afa4_SM2712_11.jpg)
0 = ![Let 0 and 1 be the intercept and slope from the regression of y i on x i , using n observations. Let c 1 and c 2 , with c 2 0, be constants. Let 0 and 1 be the intercept and slope from the regression of c 1 y i on c 2 x i. Show that 1 = (c 1 /c 2 ) 0 and 0 = c 1 0 , thereby verifying the claims on units of measurement in Section 2.4. [Hint: To obtain 1 , plug the scaled versions of x and y into (2.19). Then, use (2.17) for 0 , being sure to plug in the scaled x and y and the correct slope.] (ii) Now, let 0 and 1 be from the regression of (c 1 + y i ) on (c 2 + x i ) (with no restriction on c 1 or c 2 ). Show that l = 1 and 0 = 0 + c 1 - c 2 1. (iii) Now, let 0 and 1 be the OLS estimates from the regression log(y i ) on x i , where we must assume y i. 0 for all i. For c 1 0, let 0 and 1 be the intercept and slope from the regression of log(c 1 y i ) on x i. Show that . (iv) Now, assuming that x. 0 for all i, let 0 and 1 be the intercept and slope from the regression of y. on log(c 2 x i ). How do 0 and 1 compare with the intercept and slope from the regression of y i on log(x i )](https://storage.examlex.com/SM2712/11eb9ee2_f06c_515e_8edd_3f349b2b95f0_SM2712_11.jpg)
0 + c 1 - c 2 ![Let 0 and 1 be the intercept and slope from the regression of y i on x i , using n observations. Let c 1 and c 2 , with c 2 0, be constants. Let 0 and 1 be the intercept and slope from the regression of c 1 y i on c 2 x i. Show that 1 = (c 1 /c 2 ) 0 and 0 = c 1 0 , thereby verifying the claims on units of measurement in Section 2.4. [Hint: To obtain 1 , plug the scaled versions of x and y into (2.19). Then, use (2.17) for 0 , being sure to plug in the scaled x and y and the correct slope.] (ii) Now, let 0 and 1 be from the regression of (c 1 + y i ) on (c 2 + x i ) (with no restriction on c 1 or c 2 ). Show that l = 1 and 0 = 0 + c 1 - c 2 1. (iii) Now, let 0 and 1 be the OLS estimates from the regression log(y i ) on x i , where we must assume y i. 0 for all i. For c 1 0, let 0 and 1 be the intercept and slope from the regression of log(c 1 y i ) on x i. Show that . (iv) Now, assuming that x. 0 for all i, let 0 and 1 be the intercept and slope from the regression of y. on log(c 2 x i ). How do 0 and 1 compare with the intercept and slope from the regression of y i on log(x i )](https://storage.examlex.com/SM2712/11eb9ee2_f06c_515f_8edd_e5194530d27c_SM2712_11.jpg)
1.
(iii) Now, let![Let 0 and 1 be the intercept and slope from the regression of y i on x i , using n observations. Let c 1 and c 2 , with c 2 0, be constants. Let 0 and 1 be the intercept and slope from the regression of c 1 y i on c 2 x i. Show that 1 = (c 1 /c 2 ) 0 and 0 = c 1 0 , thereby verifying the claims on units of measurement in Section 2.4. [Hint: To obtain 1 , plug the scaled versions of x and y into (2.19). Then, use (2.17) for 0 , being sure to plug in the scaled x and y and the correct slope.] (ii) Now, let 0 and 1 be from the regression of (c 1 + y i ) on (c 2 + x i ) (with no restriction on c 1 or c 2 ). Show that l = 1 and 0 = 0 + c 1 - c 2 1. (iii) Now, let 0 and 1 be the OLS estimates from the regression log(y i ) on x i , where we must assume y i. 0 for all i. For c 1 0, let 0 and 1 be the intercept and slope from the regression of log(c 1 y i ) on x i. Show that . (iv) Now, assuming that x. 0 for all i, let 0 and 1 be the intercept and slope from the regression of y. on log(c 2 x i ). How do 0 and 1 compare with the intercept and slope from the regression of y i on log(x i )](https://storage.examlex.com/SM2712/11eb9ee2_f06c_5160_8edd_fb7c087632bf_SM2712_11.jpg)
0 and ![Let 0 and 1 be the intercept and slope from the regression of y i on x i , using n observations. Let c 1 and c 2 , with c 2 0, be constants. Let 0 and 1 be the intercept and slope from the regression of c 1 y i on c 2 x i. Show that 1 = (c 1 /c 2 ) 0 and 0 = c 1 0 , thereby verifying the claims on units of measurement in Section 2.4. [Hint: To obtain 1 , plug the scaled versions of x and y into (2.19). Then, use (2.17) for 0 , being sure to plug in the scaled x and y and the correct slope.] (ii) Now, let 0 and 1 be from the regression of (c 1 + y i ) on (c 2 + x i ) (with no restriction on c 1 or c 2 ). Show that l = 1 and 0 = 0 + c 1 - c 2 1. (iii) Now, let 0 and 1 be the OLS estimates from the regression log(y i ) on x i , where we must assume y i. 0 for all i. For c 1 0, let 0 and 1 be the intercept and slope from the regression of log(c 1 y i ) on x i. Show that . (iv) Now, assuming that x. 0 for all i, let 0 and 1 be the intercept and slope from the regression of y. on log(c 2 x i ). How do 0 and 1 compare with the intercept and slope from the regression of y i on log(x i )](https://storage.examlex.com/SM2712/11eb9ee2_f06c_5161_8edd_9b1e93ada901_SM2712_11.jpg)
1 be the OLS estimates from the regression log(y i ) on x i , where we must assume y i. 0 for all i. For c 1 0, let ![Let 0 and 1 be the intercept and slope from the regression of y i on x i , using n observations. Let c 1 and c 2 , with c 2 0, be constants. Let 0 and 1 be the intercept and slope from the regression of c 1 y i on c 2 x i. Show that 1 = (c 1 /c 2 ) 0 and 0 = c 1 0 , thereby verifying the claims on units of measurement in Section 2.4. [Hint: To obtain 1 , plug the scaled versions of x and y into (2.19). Then, use (2.17) for 0 , being sure to plug in the scaled x and y and the correct slope.] (ii) Now, let 0 and 1 be from the regression of (c 1 + y i ) on (c 2 + x i ) (with no restriction on c 1 or c 2 ). Show that l = 1 and 0 = 0 + c 1 - c 2 1. (iii) Now, let 0 and 1 be the OLS estimates from the regression log(y i ) on x i , where we must assume y i. 0 for all i. For c 1 0, let 0 and 1 be the intercept and slope from the regression of log(c 1 y i ) on x i. Show that . (iv) Now, assuming that x. 0 for all i, let 0 and 1 be the intercept and slope from the regression of y. on log(c 2 x i ). How do 0 and 1 compare with the intercept and slope from the regression of y i on log(x i )](https://storage.examlex.com/SM2712/11eb9ee2_f06c_7872_8edd_d9112f8bbdad_SM2712_11.jpg)
0 and ![Let 0 and 1 be the intercept and slope from the regression of y i on x i , using n observations. Let c 1 and c 2 , with c 2 0, be constants. Let 0 and 1 be the intercept and slope from the regression of c 1 y i on c 2 x i. Show that 1 = (c 1 /c 2 ) 0 and 0 = c 1 0 , thereby verifying the claims on units of measurement in Section 2.4. [Hint: To obtain 1 , plug the scaled versions of x and y into (2.19). Then, use (2.17) for 0 , being sure to plug in the scaled x and y and the correct slope.] (ii) Now, let 0 and 1 be from the regression of (c 1 + y i ) on (c 2 + x i ) (with no restriction on c 1 or c 2 ). Show that l = 1 and 0 = 0 + c 1 - c 2 1. (iii) Now, let 0 and 1 be the OLS estimates from the regression log(y i ) on x i , where we must assume y i. 0 for all i. For c 1 0, let 0 and 1 be the intercept and slope from the regression of log(c 1 y i ) on x i. Show that . (iv) Now, assuming that x. 0 for all i, let 0 and 1 be the intercept and slope from the regression of y. on log(c 2 x i ). How do 0 and 1 compare with the intercept and slope from the regression of y i on log(x i )](https://storage.examlex.com/SM2712/11eb9ee2_f06c_7873_8edd_d5d353bc0488_SM2712_11.jpg)
1 be the intercept and slope from the regression of log(c 1 y i ) on x i. Show that ![Let 0 and 1 be the intercept and slope from the regression of y i on x i , using n observations. Let c 1 and c 2 , with c 2 0, be constants. Let 0 and 1 be the intercept and slope from the regression of c 1 y i on c 2 x i. Show that 1 = (c 1 /c 2 ) 0 and 0 = c 1 0 , thereby verifying the claims on units of measurement in Section 2.4. [Hint: To obtain 1 , plug the scaled versions of x and y into (2.19). Then, use (2.17) for 0 , being sure to plug in the scaled x and y and the correct slope.] (ii) Now, let 0 and 1 be from the regression of (c 1 + y i ) on (c 2 + x i ) (with no restriction on c 1 or c 2 ). Show that l = 1 and 0 = 0 + c 1 - c 2 1. (iii) Now, let 0 and 1 be the OLS estimates from the regression log(y i ) on x i , where we must assume y i. 0 for all i. For c 1 0, let 0 and 1 be the intercept and slope from the regression of log(c 1 y i ) on x i. Show that . (iv) Now, assuming that x. 0 for all i, let 0 and 1 be the intercept and slope from the regression of y. on log(c 2 x i ). How do 0 and 1 compare with the intercept and slope from the regression of y i on log(x i )](https://storage.examlex.com/SM2712/11eb9ee2_f06c_7874_8edd_8bfc0719daa8_SM2712_11.jpg)
.
(iv) Now, assuming that x. 0 for all i, let![Let 0 and 1 be the intercept and slope from the regression of y i on x i , using n observations. Let c 1 and c 2 , with c 2 0, be constants. Let 0 and 1 be the intercept and slope from the regression of c 1 y i on c 2 x i. Show that 1 = (c 1 /c 2 ) 0 and 0 = c 1 0 , thereby verifying the claims on units of measurement in Section 2.4. [Hint: To obtain 1 , plug the scaled versions of x and y into (2.19). Then, use (2.17) for 0 , being sure to plug in the scaled x and y and the correct slope.] (ii) Now, let 0 and 1 be from the regression of (c 1 + y i ) on (c 2 + x i ) (with no restriction on c 1 or c 2 ). Show that l = 1 and 0 = 0 + c 1 - c 2 1. (iii) Now, let 0 and 1 be the OLS estimates from the regression log(y i ) on x i , where we must assume y i. 0 for all i. For c 1 0, let 0 and 1 be the intercept and slope from the regression of log(c 1 y i ) on x i. Show that . (iv) Now, assuming that x. 0 for all i, let 0 and 1 be the intercept and slope from the regression of y. on log(c 2 x i ). How do 0 and 1 compare with the intercept and slope from the regression of y i on log(x i )](https://storage.examlex.com/SM2712/11eb9ee2_f06c_7875_8edd_8f5513e58441_SM2712_11.jpg)
0 and ![Let 0 and 1 be the intercept and slope from the regression of y i on x i , using n observations. Let c 1 and c 2 , with c 2 0, be constants. Let 0 and 1 be the intercept and slope from the regression of c 1 y i on c 2 x i. Show that 1 = (c 1 /c 2 ) 0 and 0 = c 1 0 , thereby verifying the claims on units of measurement in Section 2.4. [Hint: To obtain 1 , plug the scaled versions of x and y into (2.19). Then, use (2.17) for 0 , being sure to plug in the scaled x and y and the correct slope.] (ii) Now, let 0 and 1 be from the regression of (c 1 + y i ) on (c 2 + x i ) (with no restriction on c 1 or c 2 ). Show that l = 1 and 0 = 0 + c 1 - c 2 1. (iii) Now, let 0 and 1 be the OLS estimates from the regression log(y i ) on x i , where we must assume y i. 0 for all i. For c 1 0, let 0 and 1 be the intercept and slope from the regression of log(c 1 y i ) on x i. Show that . (iv) Now, assuming that x. 0 for all i, let 0 and 1 be the intercept and slope from the regression of y. on log(c 2 x i ). How do 0 and 1 compare with the intercept and slope from the regression of y i on log(x i )](https://storage.examlex.com/SM2712/11eb9ee2_f06c_7876_8edd_27aca6f426ba_SM2712_11.jpg)
1 be the intercept and slope from the regression of y. on log(c 2 x i ). How do ![Let 0 and 1 be the intercept and slope from the regression of y i on x i , using n observations. Let c 1 and c 2 , with c 2 0, be constants. Let 0 and 1 be the intercept and slope from the regression of c 1 y i on c 2 x i. Show that 1 = (c 1 /c 2 ) 0 and 0 = c 1 0 , thereby verifying the claims on units of measurement in Section 2.4. [Hint: To obtain 1 , plug the scaled versions of x and y into (2.19). Then, use (2.17) for 0 , being sure to plug in the scaled x and y and the correct slope.] (ii) Now, let 0 and 1 be from the regression of (c 1 + y i ) on (c 2 + x i ) (with no restriction on c 1 or c 2 ). Show that l = 1 and 0 = 0 + c 1 - c 2 1. (iii) Now, let 0 and 1 be the OLS estimates from the regression log(y i ) on x i , where we must assume y i. 0 for all i. For c 1 0, let 0 and 1 be the intercept and slope from the regression of log(c 1 y i ) on x i. Show that . (iv) Now, assuming that x. 0 for all i, let 0 and 1 be the intercept and slope from the regression of y. on log(c 2 x i ). How do 0 and 1 compare with the intercept and slope from the regression of y i on log(x i )](https://storage.examlex.com/SM2712/11eb9ee2_f06c_7877_8edd_c914acf251cb_SM2712_11.jpg)
0 and ![Let 0 and 1 be the intercept and slope from the regression of y i on x i , using n observations. Let c 1 and c 2 , with c 2 0, be constants. Let 0 and 1 be the intercept and slope from the regression of c 1 y i on c 2 x i. Show that 1 = (c 1 /c 2 ) 0 and 0 = c 1 0 , thereby verifying the claims on units of measurement in Section 2.4. [Hint: To obtain 1 , plug the scaled versions of x and y into (2.19). Then, use (2.17) for 0 , being sure to plug in the scaled x and y and the correct slope.] (ii) Now, let 0 and 1 be from the regression of (c 1 + y i ) on (c 2 + x i ) (with no restriction on c 1 or c 2 ). Show that l = 1 and 0 = 0 + c 1 - c 2 1. (iii) Now, let 0 and 1 be the OLS estimates from the regression log(y i ) on x i , where we must assume y i. 0 for all i. For c 1 0, let 0 and 1 be the intercept and slope from the regression of log(c 1 y i ) on x i. Show that . (iv) Now, assuming that x. 0 for all i, let 0 and 1 be the intercept and slope from the regression of y. on log(c 2 x i ). How do 0 and 1 compare with the intercept and slope from the regression of y i on log(x i )](https://storage.examlex.com/SM2712/11eb9ee2_f06c_7878_8edd_fd999100bb15_SM2712_11.jpg)
1 compare with the intercept and slope from the regression of y i on log(x i )
0 and 1 be the intercept and slope from the regression of y i on x i , using n observations. Let c 1 and c 2 , with c 2 0, be constants. Let 0 and 1 be the intercept and slope from the regression of c 1 y i on c 2 x i. Show that 1 = (c 1 /c 2 ) 0 and 0 = c 1 0 , thereby verifying the claims on units of measurement in Section 2.4. [Hint: To obtain 1 , plug the scaled versions of x and y into (2.19). Then, use (2.17) for 0 , being sure to plug in the scaled x and y and the correct slope.](ii) Now, let
0 and 1 be from the regression of (c 1 + y i ) on (c 2 + x i ) (with no restriction on c 1 or c 2 ). Show that l = 1 and 0 = 0 + c 1 - c 2 1.(iii) Now, let
0 and 1 be the OLS estimates from the regression log(y i ) on x i , where we must assume y i. 0 for all i. For c 1 0, let 0 and 1 be the intercept and slope from the regression of log(c 1 y i ) on x i. Show that .(iv) Now, assuming that x. 0 for all i, let
0 and 1 be the intercept and slope from the regression of y. on log(c 2 x i ). How do 0 and 1 compare with the intercept and slope from the regression of y i on log(x i )Explanation
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(i).
Consider that: 
Average of is tim...
Introductory Econometrics 4th Edition by Jeffrey Wooldridge
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