Question: Vitamin-enriched bread. Does bread lose its vitamins when stored? Small loaves of bread were prepared with flour that was fortified with a fixed amount of vitamins. After baking, the vitamin C content of two loaves was measured. Another two loaves were baked at the same time, stored for one day, and then the vitamin C content was measured. In a similar manner, two loaves were stored for three, five, and seven days before measurements were taken. The units are milligrams per hundred grams of flour (mg/100g). Here are the data:

Condition Vitamin C (mg/100g)

Immediately after baking 47.62 49.79

One day after baking 40.45 43.46

Three days after baking 21.25 22.34

Five days after baking 13.18 11.65

Seven days after baking 8.51 8.13

We will use some regression models to examine the relationship between the vitamin C concentration (VitC) and days after baking (Days) using these data.

(a) Run a linear regression to predict VitC using Days. Report the regression equation and the test statistic for the coefficient of Days with its degrees of freedom and P-value, and summarize your conclusion.

(b) Plot VitC versus Days. Also plot the residuals from your model in part (a) versus Days. Interpret these plots.

(c) Run a multiple regression using Days and the square of Days to predict VitC. Summarize the results of all of the relevant significance tests associated with this analysis.

(d) Write a short summary comparing the results of parts (a) and (c) of this exercise. Be sure to mention the values of R² for both regressions.