Find solutions to the following problems. Be sure to include a statement about s

Question

Find solutions to the following problems. Be sure to include a statement about significance and variability between the variables.

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:

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.

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 = 5.13 s = 2.03 s = 2.90

Explanation / Answer

Let the number of coffee cups taken = n

then, the independent variable = coffee cups taken

dependent variable = stress level

For the above table :

Thus,

regression equation =>

stress = 1.2164 coffee + 0.41125

So, stress level for a person who drinks 8 cups of coffee, stress level would be:

(1.2164 * 8)+ 0.41125 = 10.142

The R-squared value suggests that the variables are quite related to each other. The p-value suggests that the number of coffee cups is a significant indicator to the stress level if the level of significance is 10%, but wouldn't be so if the level of significance is 5%.

Hope this helps. Ask if you have any doubts.

SUMMARY OUTPUT Regression Statistics Multiple R 0.851902468 R Square 0.725737815 Adjusted R Square 0.680027451 Standard Error 1.640487029 Observations 8 ANOVA df SS MS F Significance F Regression 1 42.72781385 42.72781 15.87688 0.007245258 Residual 6 16.14718615 2.691198 Total 7 58.875 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 0.411255411 1.317528277 0.312142 0.765496 -2.812620145 3.635130968 -2.812620145 3.635130968 Number of Cups of Coffee 1.216450216 0.305289456 3.98458 0.007245 0.46943383 1.963466603 0.46943383 1.963466603

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