Question

let’s say I wanted to predict Susan’s score on a health assessment based on the number of hours of physical activity she engages every week. I collected some data previously, and in my study I found that the average number of hours per week a group of people exercised was 3 hours, with a standard deviation of 0.5 hours. I also found that the average health score for these people was 15, with a standard deviation of 5 points. The correlation between exercise time and health scores was .71 (i.e., the more time people exercised, the higher the health rating). If Susan told me she exercises 5 hours per week, according to my data, what would be her predicted health score?  

Answer 1

Let X : number of hours of physical activity Susan engage every week.

Y : Susan's health score

Given , xbar = 3 , s_{​​​​​​x} = 0.5

ybar = 15 , s_{​​​​​​y}​​​ = 5

r = 0.71

First we have to find regression equation for y = bo + b1 * X

Where b1 = r *( S_{​​​​​​y}​​​​​/S_{​​​​x})

b1 = 0.71 *(5/0.5)

b1 = 7.1

bo = ybar - b1 * xbar = 15 - 7.1*3

bo = -6.3

So regression equation is y = - 6.3 + 7.1 * X

We asked if Susan exercises 5 hours per week ( X = 5) what would be her predicted health score ( y^)

y^ = -6.3 + 7.1 * 5

y^ = 29.2

So Susan's health score is 29.2