We wish to find a model to predict levels of beta-carotene in the blood, which is the variable BetaPlasma in the dataset NutritionStudy, using the following variables as potential predictors: Age, Fat, Fiber, Alcohol, and BetaDiet. The last is the amount of beta-carotene consumed by a person.

(a) Use technology to find the correlation between each of the predictors and the response variable BetaPlasma. Identify the predictors that appear to be potentially useful based on these correlations.
(b) Try different models and combinations of predictors to help explain the beta-carotene plasma levels. Try to get a good R² and a good ANOVA p-value, but also have significant predictors. Decide on a final model and briefly indicate why you chose it.