Investigation 11: Roller coasters (assigned Tues Feb 23, due Fri Feb 26)

You may work with one other person on this assignment, handing in one report with both names. Word-processed reports are much preferred to hand-written ones. Please copy/paste relevant gapminder output into a Word file as appropriate.

Reconsider the data on roller coasters (RollerCoasters.mtw). Now you are asked to consider multiple regression models for predicting the age of a roller coaster.

a) Determine (and report) the regression equation for predicting a roller coaster’s age (as of the year 2003) from 5 predictors: speed, height, length, drop, and inversions. Also report the values of R², adjusted R², and s_e.

b) Report the test statistic and p-value for the model utility test. Also summarize your conclusion from this test.

c) Identify all variables for which the p-value from the test of individual coefficients is less than .10. Also report these p-values.

d) Report and interpret the value of the coefficient of the “inversions” variable in this model.

e) Now determine (and report) the regression equation for predicting age from the single best predictor from the original five. Also submit a fitted line plot, interpret the value of the slope coefficient, and report the values of R², adjusted R², and s_e.

f) Comment on how these two regression models compare. Which do you think is the better model for predicting a roller coaster’s age? Explain.

g) Now consider other regression models for predicting age from a subset of the original five predictors. Decide which regression model you think is best, and report its regression equation along with the values of R², adjusted R², and s_e. Also report the test statistic and p-value from the model utility test and from tests of individual coefficients for this model. Finally, explain why you think this model is the best.