Assignment 6

  1. Run a least squares regression on the data, which gives violent and property Crime rates in 22 metropolitan areas, to obtain a regression of property crime rate on population. Examine various influence diagnostics and discuss what you would do. Regress violent crime rate on property crime rate and obtain influence diagnostics. State your conclusions. Do the same for a regression of violent crime rate against property crime rate and population.
  2. For the two regressions in Problem 1 (a) and (b) of Assignment 3, check whether one can assume normality of the errors and examine whether there exist observations that should be regarded as outliers?
  3. The data set gives observations on the acceleration (ACC) of different vehicles along with their weight-to-horsepower ratio (WHP), the speed at which they were traveling (SP), and the grade (G; G=0 implies the road was horizontal).
    1. Run a regression using ACC as your response without making any transformations, and obtain partial residual plot.
    2. Obtain a good fitting model by making whatever changes you think are necessary. Obtain appropriate plots to verify that you have succeeded.
    3. The partial residual plot involving SP in the question i (above) appears to show heteroscedasticity (i.e, violation of var(ε)=σ2I), If you have been successful in the question ii, the appearance of any serious heteroscedasticity should vanish without your having to weight or transform the response. Explain why you think this happens.