Find the estimated simple linear regression equation for predicting “Risk” based

ID: 3176833 • Letter: F

Question

Find the estimated simple linear regression equation for predicting “Risk” based on the person's “Age”. What is the coefficient for the slope? (Report 3 digits to the right of the decimal.)I believe this is the correct equation y=134.117+0.853*x

Risk Age Pressure Smoker 12 57 152 No 24 67 163 No 13 58 155 No 56 86 177 Yes 28 59 196 No 51 76 189 Yes 18 56 155 Yes 31 78 120 No 37 80 135 Yes 15 78 98 No 22 71 152 No 36 70 173 Yes 15 67 135 Yes 48 77 209 Yes 15 60 199 No 36 82 119 Yes 8 66 166 No 34 80 125 Yes 3 62 117 No 37 59 207 Yes

Explanation / Answer

Back-up Theory

Let X = age, Y = risk and regression of Y on X is: y = a + bx.

Then, b = SXY/SXX and a = Ybar – b.Xbar, where

Xbar = (1/n)sum of xi over I = 1, 2, …., n; Ybar = (1/n)sum of yi over I = 1, 2, …., n;

Sxx = sum of (xi – Xbar)2 over i = 1, 2, …., n and

SxY = sum of (xi – Xbar)(y - Ybar) over i = 1, 2, …., n

Now, to work out solution,

From the given data, the following have been computed:

X Bar

26.95

Sxx

4190.95

Y Bar

69.45

Sxy

1139.275

0.271842

62.12387

So, the estimated simple linear regression equation for predicting “Risk”(y) based on the person's “Age”(x) is

y = 62.124 + 0.272x and the coefficient for the slope is 0.272 (b) ANSWER