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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 8
Let ![Let 0 and l be the OLS intercept and slope estimators, respectively, and let u be the sample average of the errors (not the residuals!). (i) Show that B1 can be written as = B1 + V.. w.u. where w. = d./SST and d. = x. - x. ==1 w. = 0, to show that B1 and u are uncorrelated. [Hint: You are being asked to show that E[(fi1 - B1). u] = 0.] (iii) Show that B0 can be written as .w i u i where w i =d i /SST X and d i = x i - (iv) Use parts (i) along with to show that 1 and are uncorrelated. [Hint: You are being asked to show that (iii) show that 0 can be written as (iv). Use parts (ii) and (iii) to show that (v) Do the algebra to simplify the expression in part (iv) to equation (2.58). [Hint:](https://d2lvgg3v3hfg70.cloudfront.net/SM2712/11eb9ee2_f06d_8a0b_8edd_514fdb02ba02_SM2712_11.jpg)
0 and ![Let 0 and l be the OLS intercept and slope estimators, respectively, and let u be the sample average of the errors (not the residuals!). (i) Show that B1 can be written as = B1 + V.. w.u. where w. = d./SST and d. = x. - x. ==1 w. = 0, to show that B1 and u are uncorrelated. [Hint: You are being asked to show that E[(fi1 - B1). u] = 0.] (iii) Show that B0 can be written as .w i u i where w i =d i /SST X and d i = x i - (iv) Use parts (i) along with to show that 1 and are uncorrelated. [Hint: You are being asked to show that (iii) show that 0 can be written as (iv). Use parts (ii) and (iii) to show that (v) Do the algebra to simplify the expression in part (iv) to equation (2.58). [Hint:](https://d2lvgg3v3hfg70.cloudfront.net/SM2712/11eb9ee2_f06d_b11c_8edd_4135c6a4d4ac_SM2712_11.jpg)
l be the OLS intercept and slope estimators, respectively, and let u be the sample average of the errors (not the residuals!).
(i) Show that B1 can be written as = B1 + V.. w.u. where w. = d./SST and d. = x. - x.
==1 w. = 0, to show that B1 and u are uncorrelated. [Hint: You are being asked to show that E[(fi1 - B1). u] = 0.]
(iii) Show that B0 can be written as![Let 0 and l be the OLS intercept and slope estimators, respectively, and let u be the sample average of the errors (not the residuals!). (i) Show that B1 can be written as = B1 + V.. w.u. where w. = d./SST and d. = x. - x. ==1 w. = 0, to show that B1 and u are uncorrelated. [Hint: You are being asked to show that E[(fi1 - B1). u] = 0.] (iii) Show that B0 can be written as .w i u i where w i =d i /SST X and d i = x i - (iv) Use parts (i) along with to show that 1 and are uncorrelated. [Hint: You are being asked to show that (iii) show that 0 can be written as (iv). Use parts (ii) and (iii) to show that (v) Do the algebra to simplify the expression in part (iv) to equation (2.58). [Hint:](https://d2lvgg3v3hfg70.cloudfront.net/SM2712/11eb9ee2_f06d_b11d_8edd_bd3be47b92eb_SM2712_11.jpg)
.w i u i where w i =d i /SST X and d i = x i - ![Let 0 and l be the OLS intercept and slope estimators, respectively, and let u be the sample average of the errors (not the residuals!). (i) Show that B1 can be written as = B1 + V.. w.u. where w. = d./SST and d. = x. - x. ==1 w. = 0, to show that B1 and u are uncorrelated. [Hint: You are being asked to show that E[(fi1 - B1). u] = 0.] (iii) Show that B0 can be written as .w i u i where w i =d i /SST X and d i = x i - (iv) Use parts (i) along with to show that 1 and are uncorrelated. [Hint: You are being asked to show that (iii) show that 0 can be written as (iv). Use parts (ii) and (iii) to show that (v) Do the algebra to simplify the expression in part (iv) to equation (2.58). [Hint:](https://d2lvgg3v3hfg70.cloudfront.net/SM2712/11eb9ee2_f06d_b11e_8edd_e52aa77f52d7_SM2712_11.jpg)
(iv) Use parts (i) along with![Let 0 and l be the OLS intercept and slope estimators, respectively, and let u be the sample average of the errors (not the residuals!). (i) Show that B1 can be written as = B1 + V.. w.u. where w. = d./SST and d. = x. - x. ==1 w. = 0, to show that B1 and u are uncorrelated. [Hint: You are being asked to show that E[(fi1 - B1). u] = 0.] (iii) Show that B0 can be written as .w i u i where w i =d i /SST X and d i = x i - (iv) Use parts (i) along with to show that 1 and are uncorrelated. [Hint: You are being asked to show that (iii) show that 0 can be written as (iv). Use parts (ii) and (iii) to show that (v) Do the algebra to simplify the expression in part (iv) to equation (2.58). [Hint:](https://d2lvgg3v3hfg70.cloudfront.net/SM2712/11eb9ee2_f06d_b11f_8edd_e98bd4afcfea_SM2712_11.jpg)
to show that ![Let 0 and l be the OLS intercept and slope estimators, respectively, and let u be the sample average of the errors (not the residuals!). (i) Show that B1 can be written as = B1 + V.. w.u. where w. = d./SST and d. = x. - x. ==1 w. = 0, to show that B1 and u are uncorrelated. [Hint: You are being asked to show that E[(fi1 - B1). u] = 0.] (iii) Show that B0 can be written as .w i u i where w i =d i /SST X and d i = x i - (iv) Use parts (i) along with to show that 1 and are uncorrelated. [Hint: You are being asked to show that (iii) show that 0 can be written as (iv). Use parts (ii) and (iii) to show that (v) Do the algebra to simplify the expression in part (iv) to equation (2.58). [Hint:](https://d2lvgg3v3hfg70.cloudfront.net/SM2712/11eb9ee2_f06d_b120_8edd_fb9ac614f637_SM2712_11.jpg)
1 and ![Let 0 and l be the OLS intercept and slope estimators, respectively, and let u be the sample average of the errors (not the residuals!). (i) Show that B1 can be written as = B1 + V.. w.u. where w. = d./SST and d. = x. - x. ==1 w. = 0, to show that B1 and u are uncorrelated. [Hint: You are being asked to show that E[(fi1 - B1). u] = 0.] (iii) Show that B0 can be written as .w i u i where w i =d i /SST X and d i = x i - (iv) Use parts (i) along with to show that 1 and are uncorrelated. [Hint: You are being asked to show that (iii) show that 0 can be written as (iv). Use parts (ii) and (iii) to show that (v) Do the algebra to simplify the expression in part (iv) to equation (2.58). [Hint:](https://d2lvgg3v3hfg70.cloudfront.net/SM2712/11eb9ee2_f06d_b121_8edd_bd12bcb6cd50_SM2712_11.jpg)
are uncorrelated. [Hint: You are being asked to show that ![Let 0 and l be the OLS intercept and slope estimators, respectively, and let u be the sample average of the errors (not the residuals!). (i) Show that B1 can be written as = B1 + V.. w.u. where w. = d./SST and d. = x. - x. ==1 w. = 0, to show that B1 and u are uncorrelated. [Hint: You are being asked to show that E[(fi1 - B1). u] = 0.] (iii) Show that B0 can be written as .w i u i where w i =d i /SST X and d i = x i - (iv) Use parts (i) along with to show that 1 and are uncorrelated. [Hint: You are being asked to show that (iii) show that 0 can be written as (iv). Use parts (ii) and (iii) to show that (v) Do the algebra to simplify the expression in part (iv) to equation (2.58). [Hint:](https://d2lvgg3v3hfg70.cloudfront.net/SM2712/11eb9ee2_f06d_b122_8edd_7143f6e34977_SM2712_11.jpg)
(iii) show that![Let 0 and l be the OLS intercept and slope estimators, respectively, and let u be the sample average of the errors (not the residuals!). (i) Show that B1 can be written as = B1 + V.. w.u. where w. = d./SST and d. = x. - x. ==1 w. = 0, to show that B1 and u are uncorrelated. [Hint: You are being asked to show that E[(fi1 - B1). u] = 0.] (iii) Show that B0 can be written as .w i u i where w i =d i /SST X and d i = x i - (iv) Use parts (i) along with to show that 1 and are uncorrelated. [Hint: You are being asked to show that (iii) show that 0 can be written as (iv). Use parts (ii) and (iii) to show that (v) Do the algebra to simplify the expression in part (iv) to equation (2.58). [Hint:](https://d2lvgg3v3hfg70.cloudfront.net/SM2712/11eb9ee2_f06d_d833_8edd_09d548ee8cbd_SM2712_11.jpg)
0 can be written as ![Let 0 and l be the OLS intercept and slope estimators, respectively, and let u be the sample average of the errors (not the residuals!). (i) Show that B1 can be written as = B1 + V.. w.u. where w. = d./SST and d. = x. - x. ==1 w. = 0, to show that B1 and u are uncorrelated. [Hint: You are being asked to show that E[(fi1 - B1). u] = 0.] (iii) Show that B0 can be written as .w i u i where w i =d i /SST X and d i = x i - (iv) Use parts (i) along with to show that 1 and are uncorrelated. [Hint: You are being asked to show that (iii) show that 0 can be written as (iv). Use parts (ii) and (iii) to show that (v) Do the algebra to simplify the expression in part (iv) to equation (2.58). [Hint:](https://d2lvgg3v3hfg70.cloudfront.net/SM2712/11eb9ee2_f06d_d834_8edd_37278262d0b9_SM2712_11.jpg)
(iv). Use parts (ii) and (iii) to show that![Let 0 and l be the OLS intercept and slope estimators, respectively, and let u be the sample average of the errors (not the residuals!). (i) Show that B1 can be written as = B1 + V.. w.u. where w. = d./SST and d. = x. - x. ==1 w. = 0, to show that B1 and u are uncorrelated. [Hint: You are being asked to show that E[(fi1 - B1). u] = 0.] (iii) Show that B0 can be written as .w i u i where w i =d i /SST X and d i = x i - (iv) Use parts (i) along with to show that 1 and are uncorrelated. [Hint: You are being asked to show that (iii) show that 0 can be written as (iv). Use parts (ii) and (iii) to show that (v) Do the algebra to simplify the expression in part (iv) to equation (2.58). [Hint:](https://d2lvgg3v3hfg70.cloudfront.net/SM2712/11eb9ee2_f06d_d835_8edd_07b91da00ad8_SM2712_11.jpg)
(v) Do the algebra to simplify the expression in part (iv) to equation (2.58). [Hint:![Let 0 and l be the OLS intercept and slope estimators, respectively, and let u be the sample average of the errors (not the residuals!). (i) Show that B1 can be written as = B1 + V.. w.u. where w. = d./SST and d. = x. - x. ==1 w. = 0, to show that B1 and u are uncorrelated. [Hint: You are being asked to show that E[(fi1 - B1). u] = 0.] (iii) Show that B0 can be written as .w i u i where w i =d i /SST X and d i = x i - (iv) Use parts (i) along with to show that 1 and are uncorrelated. [Hint: You are being asked to show that (iii) show that 0 can be written as (iv). Use parts (ii) and (iii) to show that (v) Do the algebra to simplify the expression in part (iv) to equation (2.58). [Hint:](https://d2lvgg3v3hfg70.cloudfront.net/SM2712/11eb9ee2_f06d_d836_8edd_a1093b482ea7_SM2712_11.jpg)
0 and l be the OLS intercept and slope estimators, respectively, and let u be the sample average of the errors (not the residuals!).(i) Show that B1 can be written as = B1 + V.. w.u. where w. = d./SST and d. = x. - x.
==1 w. = 0, to show that B1 and u are uncorrelated. [Hint: You are being asked to show that E[(fi1 - B1). u] = 0.]
(iii) Show that B0 can be written as
.w i u i where w i =d i /SST X and d i = x i - (iv) Use parts (i) along with
to show that 1 and are uncorrelated. [Hint: You are being asked to show that (iii) show that
0 can be written as (iv). Use parts (ii) and (iii) to show that
(v) Do the algebra to simplify the expression in part (iv) to equation (2.58). [Hint:
Explanation
Verified
Verified
Consider 
are the OLS intercept and slop...
Introductory Econometrics 4th Edition by Jeffrey Wooldridge
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