3. 6 Points) The population from which the sample was selected consists of execu

Question

3. 6 Points) The population from which the sample was selected consists of executives between the ages of 24 and 60 who are working in U.S. manufacturing business. Let annual salary in 1,000 dollars (Y) be the dependent variable and age (X) be the independent variable. Show me your work. DO NOT UUSE Excel!!! Sala X-X bar Y-Ybar Xbar)2 (Y-Ybar)A2 Person 65 85 74 83 110 160 100 122 85 120 105 135 125 175 156 140 1840 115 26 28 Lo 35 Philli Massa Saas 42 45 46 Malroon Kirn Tom Jane Charles 51 Daniel Sum 61 63 704 a. Calculate the sample covariance between Y and X (s). b. Calculate the sample coefficient of correlation between Y and X Suppose that we measure salary in dollars, not in 1000 dollars. Let this be Z. Then, if we calculate the correlation coefficient between Z and X, do we still find the same correlation coefficient as in the above (part b)? Explain. c. d. Use the method of least squares to compute an estimated regression line between Y and X. (b and bo)

Explanation / Answer

(a)sxy=sum(X-Xbar)(Y-Ybar)/(n-1)=3594/(16-1)=239.6

(b)s2x=sum(X-Xbar)2/(n-1)=1732/15=115.47, s2y=1057.33

sample correlation coefficient=r=sxy/sx*sy=239.6/sqrt(115.47*1057.33)=0.6857

(c) corrleation coefficient will be same as it is indendent of origin and scale

(d)y=a+bx=23.48+2.08*x

least square estimate of a and b are

b=r*sy/sx=0.6857*sqrt(1057.33/115.47)=2.08

a=mean(y)-b*mean(x)=115-2.08*44=23.48

following information has been generated using ms-excel

X Y X-Xbar Y-bar (X-Xbar)(Y-Ybar) (X-Xbar)2 (Y-Ybar)2 26 65 -18 -50 900 324 2500 28 85 -16 -30 480 256 900 36 74 -8 -41 328 64 1681 35 83 -9 -32 288 81 1024 35 110 -9 -5 45 81 25 40 160 -4 45 -180 16 2025 41 100 -3 -15 45 9 225 42 122 -2 7 -14 4 49 45 85 1 -30 -30 1 900 46 120 2 5 10 4 25 50 105 6 -10 -60 36 100 51 135 7 20 140 49 400 55 125 11 10 110 121 100 50 175 6 60 360 36 3600 61 156 17 41 697 289 1681 63 140 19 25 475 361 625 sum 704 1840 0 0 3594 1732 15860 mean 44 115 0 0 224.625 108.25 991.25

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