Question

A psychologist wants to determine if there is a linear relationship between the number of hours a person goes without sleep and the number of mistakes he/she makes on a simple test. The following data is recorded. Determine the equation of the regression line and graph the line on a scatter plot. Hours without Sleep, x Number of Mistakes, y

x y

32 6

38 8

48 13

24 5

46 7

35 6

30 5

34 8

42 12

Now, pretend in this problem that you did not reject the null hypothesis and you could no create a regression line. What value would you predict for the number of mistakes if your hours without sleep was 40.

Answer 1

Here we have data:

X	Y
32	6
38	8
48	13
24	5
46	7
35	6
30	5
34	8
42	12

Here we are using Excel for calculation:

Scatter plot:

14 13 y 0.2885x-2.7677 R2 0.594 12 11 10 9 8 7 6 5 4 40 20 25 30 35 45 50

Regression equation:

Y = -2.7677 + 0.2885X

X = 40

Y = -2.7677 + 0.2885 * 40

= 8.7723