statistics

In a study of caffeine and stress, college students indicate how many cups of coffee they drink per day and their stress level on a scale of 1-10. The data appear below.
Number of Cups of Coffee
Stress Level

3
5

2
3

4
3

6
9

5
4

1
2

7
10

3
5

= 3.88
X= 5.13

s = 2.03
s = 2.90

Determine the regression equation for predicting stress level from the amount of coffee per day one consumes.
Predict the stress level for someone who drinks 8 cups of coffee a day.

1. MathGuru

If you need to show the work by hand, you can develop the regression equation in the following format:

predicted y = a + bx
...where a represents the y-intercept and b the slope.

To get to that point, here are some formulas to calculate along the way.

To find a:
a = (Ey/n) - b(Ex/n)

Note: E means to add up or to find the total.

To find b:
b = SSxy/SSxx

To find SSxy:
SSxy = Exy - [(Ex)(Ey)]/n

To find SSxx:
SSxx = Ex^2 - [(Ex)(Ex)]/n

Note: x = cups of coffee; y = stress level

Once you have the equation, substitute 8 for x, then solve for predicted y.

I hope this will help get you started.

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