Is depression a possible factor in students missing classes? In Data D.1 on page 599, we introduce the data in SleepStudy. Two of the variables in that study are DepressionScore, scores on a standard depression scale with higher numbers indicating greater depression, and ClassesMissed, the number of classes missed during the semester. Computer output is shown for predicting the number of classes missed based on the depression score.

Residual standard error: 3.208 on 251 degrees of freedom
Multiple R-squared: 0.0237, Adjusted R-squared: 0.01981
F-statistic: 6.092 on 1 and 251 DF, p-value: 0.01424

(a) Interpret the slope of the regression line in context.

(b) Identify the t-statistic and the p-value for testing the slope. What is the conclusion, at a 5% level?

(c) Interpret R² in context.

(d) Identify the F-statistic and p-value from the ANOVA for regression. What is the conclusion of that test?

Data D.1 on page 599

A recent study examines the relationship between class start times, sleep, circadian preference, alcohol use, academic performance, and other variables in college students. The data were obtained from a sample of students who did skills tests to measure cognitive function, completed a survey that asked many questions about attitudes and habits, and kept a sleep diary to record time and quality of sleep over a two-week period. Some data from this study are available in SleepStudy.

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Coefficients: Pr(> [t]) 6.652 1.79e-10 0.0142 Estimate Std. Error t value 1.77712 0.08312 (Intercept) 0.26714 *** 2.468 DepressionScore 0.03368