FILE Nutritional_Facts. R Jenny, a first-year Nutrition Studies student at Hillside College, is conducting research on various common food items and their nutritional facts. She compiled a data set that contains the nutrition facts on 30 common food items. Jenny feels that many of the nutritional facts of these food items are highly correlated and wonders if there is a way to reduce the dimensionality of the data set by creating principal components. a. Conduct principal component analysis on all the variables except the Name variable. Should you standardize the data? Explain. How many principal components are computed? b. What percent of the total variability is accounted for by the first principal component? c. Display the weights used to compute the first principal component scores. d. Create a new data set that contains the names of the food items and the principal components that account for at least 80% of the total variance in the data. How many principal components must be retained in order to account for at least 80% of the total variance in the data? FILE Nutritional_Facts. R Jenny, a first-year Nutrition Studies student at Hillside College, is conducting research on various common food items and their nutritional facts. She compiled a data set that contains the nutrition facts on 30 common food items. Jenny feels that many of the nutritional facts of these food items are highly correlated and wonders if there is a way to reduce the dimensionality of the data set by creating principal components. a. Conduct principal component analysis on all the variables except the Name variable. Should you standardize the data? Explain. How many principal components are computed? b. What percent of the total variability is accounted for by the first principal component? c. Display the weights used to compute the first principal component scores. d. Create a new data set that contains the names of the food items and the principal components that account for at least 80% of the total variance in the data. How many principal components must be retained in order to account for at least 80% of the total variance in the data