The data in CommuteAtlanta show information on both the commute distance (in miles) and time (in minutes) for a sample of 500 Atlanta commuters. Suppose that we want to build a model for predicting the commute time based on the distance.
(a) Fit the simple linear model, Time = β₀ + β₁ Distance + є, for the sample of Atlanta commuters and write down the prediction equation.
(b) What time (in minutes) does the fitted model predict for a 20 mile commute?
(c) Produce a scatterplot of the relationship between Time and Distance and comment on any interesting patterns in the plot.
(d) Produce a dotplot or histogram to show the distribution of the residuals for this model. Comment on whether the normality condition is reasonable.
(e) Produce a plot of the residuals vs the fitted values. Comment on what this plot says about the simple linear model conditions in this situation.

Data in CommuteAtlanta

What is the average commuting time for people who live and work in the Atlanta metropolitan area? It’s not very feasible to contact all Atlanta residents and ask about their commutes, but the US Census Bureau regularly collects data from carefully selected samples of residents in many areas. One such data source is the American Housing Survey (AHS), which contains information about housing and living conditions for samples from the country as a whole and certain metropolitan areas. The data in CommuteAtlanta includes cases where the respondent worked somewhere other than home in the Atlanta metropolitan area. Among the questions asked were the time (in minutes) and distance (in miles) that respondents typically traveled on their commute to work each day.