Researchers have examined a number of climatic variables in an attempt to understand the mechanisms that govern rainfall runoff. The paper “The Applicability of Morton’s and Penman’s Evapotranspiration Estimates in Rainfall-Runoff Modeling” (Water Resources Bulletin [1991]: 611–620) reported on a study that examined the relationship between x = cloud cover index and y = sunshine index. The cloud cover index can have values between 0 and 1. The accompanying data are consistent with summary quantities in the article. The authors of the article used a cubic regression to describe the relationship between cloud cover and sunshine.
a. Construct a scatterplot of the data. What characteristics of the plot suggest that a cubic regression would be more appropriate for summarizing the relationship between sunshine index and cloud cover index than a linear or quadratic regression?
b. Find the equation of the least-squares cubic function. y^ = = 10.8768 + 1.4604x - 7.259x2 + 9.2342x3

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