The quality of sleep is measured by factors such as heart rate, blood pressure, REM cycle interval, etc. The file SleepQuality contains data about the sleep duration (in minutes) and sleep quality scores (in percent) is for 50 people. You want to examine whether sleep duration has an effect on the quality of sleep.

a. Assuming a linear relationship, use the least-squares method to compute the regression coefficients b₀ and b₁.

b. Interpret the meaning of the slope, b₁, in this problem.

c. Predict the mean sleep quality score of people who sleep 8 hours.

d. Determine the coefficient of determination, r², and interpret its meaning.

e. Perform a residual analysis and evaluate the regression assumptions.

f. At the 0.05 level of significance, is there evidence of a linear relationship between sleep duration and sleep quality score?

g. Construct a 95% confidence interval estimate of the population slope, b₁.