Question

Please provide the full derivation of the answers. Thank you!

Q8) 1 Point for part a, 1 point for part b; total 2 points A professor in the School of Business in a university polled a dozen colleagues about the number of professional meetings they attended in the past five years (x) and the number of papers they submitted to refereed journals (y) during the same period. The summary data are given as follows: n = 12, x = 4, y = 12,2= x =232,2 xy=318 a) Fit a simple linear regression model between x and y by finding out the estimates of intercept and slope. b) Comment on whether attending more professional meetings would result in publishing more papers.

Answer 1

Solution . Given Data A Professor in the school of Business in a uni university Pohled o dozen colleagues about the number of Professional meetings they attended in the past five years (x) and the number of papers they submitted to refereed journals (4) same period. during the 5=4 n = 12, y = 12 2 at = 232 2 x; 4; = 318 fit a simple linear regression model between x and y by finding out the estimates of intercept and slope. Data given êxi = nx isl

whimp na 12, X = 4 12x4 = 48 n X; = 48 § 4; ny is! where na 12, Y = 12 12x12 144 luy sw.l Yi- The linear regression curve is Myla Bo + Bx The above linear regression curve is the last seases

3 estimates be and be of the ne gression coefficients Bo and B, are computed by the bollucing tolmul as is step 0: ng x14 -(x) (0,4) bia n n X; X; where n=12, 2. x; 4;= 318, 2. *;= 48 ا=ز n 2 4; = 144, { Xi = 232, i=1 iel 12 x (318) (48 x 144) 12 x 232 (48)2 3816 6912 - 2784 2304 - 3096 480 - 6.45

4 bis -6.45 step : , 4;- b. (Êxi) ial bo= n where n=12, 4; = 144, bı= -6.45, X; = 48 144 (-6.45) x ( 48') bo 12 144 309.6 12 453.6 12 37.8 bo 37.8 The bitted simple linear regression model between y and y is (.: Myx= Bo+Bix) M ŷ = 37.8 6.450 Ylx

5 6 comment on whether attending mone professional more papers. meetings would result in publishing The bitted simple linear regression model Myly = 37.8 - 6.45 x so the attending more Professional meetings would result in Pullishing Sewer Popers