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.

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.

To determine the regression equation for predicting the stress level from the amount of coffee consumed, you can use the given data points. Regression analysis helps establish a relationship between two variables, in this case, the number of cups of coffee and stress level.

Here are the steps to determine the regression equation:

1. Calculate the mean values for both the number of cups of coffee and the stress level. The mean of the number of cups of coffee is 3.88, and the mean stress level is 5.13.

2. Calculate the deviation of each data point from the mean for both variables. For example:
- For the first data point, the deviation from the mean for the number of cups of coffee is 3 - 3.88 = -0.88, and the deviation from the mean for the stress level is 5 - 5.13 = -0.13.

3. Calculate the product of the deviations for each data point. For example:
- For the first data point, the product of deviations is (-0.88) * (-0.13) = 0.1144.

4. Calculate the sum of the products of deviations. For example:
- The sum of the products of deviations for all data points is 0.1144 + ... (continue this calculation for all data points).

5. Calculate the sum of the squared deviations for the number of cups of coffee. For example:
- For the first data point, the squared deviation for the number of cups of coffee is (-0.88)^2 = 0.7744.

6. Calculate the sum of the squared deviations for the stress level. For example:
- For the first data point, the squared deviation for the stress level is (-0.13)^2 = 0.0169.

7. Calculate the regression coefficient (b), which is the ratio of the sum of the products of deviations to the sum of the squared deviations for the number of cups of coffee.

8. Calculate the y-intercept (a), which is the mean stress level minus the product of the regression coefficient and the mean number of cups of coffee.

9. The regression equation is in the form of y = a + bx, where y is the stress level and x is the number of cups of coffee.

Now, to predict the stress level for someone who drinks 8 cups of coffee a day, you can substitute the value of x (number of cups of coffee) in the regression equation and solve for y (stress level).