3. A researcher wants to examine the relationship between the number of hours pe

Question

3. A researcher wants to examine the relationship between the number of hours people exercise per week and how long they live (longevity 20 adults over 65 is given below ). The data on a random sample of hours exercisedLongevity 0 0 0 70 68 75 76 72 69 73 72 74 72 4 4 6 10 10 12 17 20 24 30 32 73 76 78 81 82 86 89 You are given mean(x) = 9.9, mean(y) = 75.3, Cov(x,y) 51.61 and the Var(X) = 95.88 Calculate the regression coefficients and interpret them? State the regression model and use it to predict the longevity of someone who exercises for 23 hours per week.

Explanation / Answer

3.

i.

calculation procedure for regression

mean of X = X / n = 9.9

mean of Y = Y / n = 75.3

(Xi - Mean)^2 = 1821.8

(Yi - Mean)^2 = 646.2

(Xi-Mean)*(Yi-Mean) = 980.6

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

= 980.6 / 1821.8

= 0.538

bo = Y / n - b1 * X / n

bo = 75.3 - 0.538*9.9 = 69.971

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

Y'=69.971+0.538* X

ii.

someone who exercise 23 hours per week

predict longevity Y =?

Y'=69.971+0.538* X

Y' = 69.971+0.538*23

Y' = 82.345

Line of Regression Y on X i.e Y = bo + b1 X X Y (Xi - Mean)^2 (Yi - Mean)^2 (Xi-Mean)*(Yi-Mean) 0 70 98.01 28.09 52.47 0 68 98.01 53.29 72.27 0 75 98.01 0.09 2.97 2 66 62.41 86.49 73.47 2 76 62.41 0.49 -5.53 3 72 47.61 10.89 22.77 4 69 34.81 39.69 37.17 4 73 34.81 5.29 13.57 6 72 15.21 10.89 12.87 6 74 15.21 1.69 5.07 8 72 3.61 10.89 6.27 8 77 3.61 2.89 -3.23 10 73 0.01 5.29 -0.23 10 77 0.01 2.89 0.17 12 76 4.41 0.49 1.47 17 78 50.41 7.29 19.17 20 81 102.01 32.49 57.57 24 82 198.81 44.89 94.47 30 86 404.01 114.49 215.07 32 89 488.41 187.69 302.77

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