Breakfast cereals are big business. According to Choice magazine, in 2011 '...we spent $1.17 billion on ready-to-eat cereal, and munched our way through 169,470 tonnes of it - that's about 10 large (750g) boxes for every man, woman and child...' But are breakfast cereals healthy? One variable of particular interest is the amount of sugar, which plays an important role in the tastiness of the product but can make for a less than healthy breakfast. The data file for this exercise contains nutritional information and ratings for 77 breakfast cereals.

(a) Apply the log transformation to variable rating to creat a new variable Lrating. Check Normality of rating and Lrating and briefly discuss the effect of the log transformation on the distribution.

(b) Obtain a Pearson correlation matrix relating variables Lrating, sugars, fiber and sodium, and comment briefly on these correlations.

(c) Obtain a scatterplot matrix relating Lrating, sugars, fiber and sodium, and briefly discuss the resulting relationships. Based on your scatterplots and results from part (b), which variable would you recommend as the single explanatory variable in a simple linear regression model for Lrating.

(d) Fit a simple linear regression model relating Lrating to the variable you have identified in part (c), with Lrating as the dependent variable. Interpret the model equation. Obtain and discuss fit diagnostics. Are there any observations that would require closer inspection? Explain briefly.