The file movie budgets.txt contains data on the budgets of 5,183 movies from 1906 to 2005, along with their lengths in minutes. Read your data into R as a data frame called movie budgets. We wish to study log10(budget) as the response variable and year and length as explanatories.
Questions:
1. Using loess or otherwise, fit a model to predict log10(budget) from year and length. For simplicity, do not transform year and length (even though a transformation of length would probably be sensible.) You will have to make a number of modeling choices:
- Should you fit a linear or curved function for year?
- Should you fit a linear or curved function for length?
- Do you need an interaction between year and length?
- What span should you use in your loess smoother?
- Should you fit using least squares or a robust fit?
Some of these choices are clear-cut, while others will be a matter of preference. Either way, you must justify all your choices.
2. Draw ONE set of faceted plots to display the fit — either condition on year or length, whichever seems to you to be more interesting. Choose a sensible number of panels. Briefly describe what this set of plots shows you.
3. Draw a raster-and-contour plot (or other “3D” plot of your choice) to further display your fit. Briefly describe what, if anything, this plot shows you that your plot for question 2 didn’t.