Suppose you have measure two variables, x and y, for a grouop of individuals, an

Question

Suppose you have measure two variables, x and y, for a grouop of individuals, and decided to make x the explanatory variable and y the response variable. Suppose the mean value of x is 20 and its standard deviation is 5; the mean value of y is 80 and its standard deviation is 20; and the correlation between x and y is .75. a.) give the equation of the least square regression line and demonstrate how you obtain it. b.) what value of y will it predict for x=25? c.) What value of x will it predict for y= 140?

Explanation / Answer

a) for slope b1 =r*sy/sx =0.75*20/5=3

and intercept bo =Ybar-b1*xbar =80-3*20=20

therefore line equation :yhat =20+3x

(ii)

for x=25 ; predicted y =20+3*25=95

(iii) for y=140 ; x =(140-20)/3 =40 ; however we should not predict independent variable from dependent variable

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