his Question: 1 pt 20 of 20 (19c Find the equation of the regression line for th

Question

his Question: 1 pt 20 of 20 (19c Find the equation of the regression line for the given data Then construct a scatter plot of the data and draw the regression line (The pair of vanablies have a sant correlation.) Then use the regression equation to predict the value of y for each of the given x-values, if meaningul The number of hours 6 students spent for est tours spent studying est score, y 1 35 43 2 52 (a) x = 2 hours (c)x-14 hours (B) x=25hours d) x-3 5 hours 2 51 61 70 to two O A. B. oc. Wh

Explanation / Answer

calculation procedure for regression

mean of X = X / n = 3.1667

mean of Y = Y / n = 52

(Xi - Mean)^2 = 14.833

(Yi - Mean)^2 = 776

(Xi-Mean)*(Yi-Mean) = 96

b1 = (Xi-Mean)*(Yi-Mean) / (Xi - Mean)^2

= 96 / 14.833

= 6.472

bo = Y / n - b1 * X / n

bo = 52 - 6.472*3.1667 = 31.505

value of regression equation is, Y = bo + b1 X

Y'=31.505+6.472* X

a.

when x = 2 hours then

Y' = 31.505+6.472* 2 = 44.449

Y' = 44.44

b.

when x = 2.5 hours then

Y' = 31.505+6.472* 2.5 = 47.685

Y' = 47.68

c.

when x = 14 hours then

Y' = 31.505+6.472* 14 = 122.113

Y' = 122.11

d.

when x = 3.5 hours then

Y' = 31.505+6.472* 3.5 = 54.157

Y' =54.15

graph below shown is option B

Line of Regression Y on X i.e Y = bo + b1 X X Y (Xi - Mean)^2 (Yi - Mean)^2 (Xi-Mean)*(Yi-Mean) 1 35 4.695 289 36.834 2 43 1.361 81 10.5 2 52 1.361 0 0 4 51 0.694 1 -0.833 5 61 3.361 81 16.5 5 70 3.361 324 32.999

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