1. Suppose you were asked to investigate which predictors explain the number of minutes that 10- to18-year-old students spend on Twitter. To do so, you build a linear regression model with Twitter usage (Y) measured as the number of minutes per week. The four predictors you include in the model are Height, Weight, Grade Level, and Age of each student. You build four simple linear regression models with Y regressed separately on each predictor, and each predictor is statistically significant. Then you build a multiple linear regression model with Y regressed on all four predictors, but only one predictor, Age, is statistically significant, and the others are not. What is likely going on among the four predictors? If you include more than one of these predictors in the model, what are some problems that can result?

2. After building a regression model and performing residual diagnostics, you notice that the errors show severe departures from normality and appear to have non-constant variance. What steps would you take in this case to resolve the errors? If the problems are not corrected after all steps are taken, what does that imply about the modeling approach you are taking? Explain in detail.