Stat 2000, Section 001, Homework Assignment 5 (30 Points)

(2/14/2015 - Due Friday 2/20/2015 by 9:35am)

• 0) Reading: Section 2.3, 2.4 & 2.5
  
  
• 1) Please work on the following textbook exercises in Moore/McCabe/Craig:
  
  
  • Exercise 2.78 (5 points) 2.102 (5), 2.103 (2), 2.110 (5), 2.113 (3)
    
    Data: http://www.math.usu.edu/~symanzik/teaching/2015_stat2000/naepmath.xls
    
    Data: http://www.math.usu.edu/~symanzik/teaching/2015_stat2000/infantgrowth.xls
    
    Data: http://www.math.usu.edu/~symanzik/teaching/2015_stat2000/siliconisotope.xls
    
    
• 2) Cereals and Calories (10 points):
  The file http://www.math.usu.edu/~symanzik/teaching/2015_stat2000/Cereals.csv contains data for 77 different breakfast cereals. It was originally posted on StatCrunch by butler@utsc.utoronto.ca on June 11, 2014.
  
  For this exercise, we are primarily interested in the question how calories in cereals are affected by five other variables, in particular fat, sugar, vitamins, potassium, and rating.
  
  You should do this as follows:
  • Calculate the correlations between calories and the five other variables of interest. Which are strongest and which are weaker? What are the directions?
  • Create the scatterplots for calories (the response variable) and the five other variables of interest. Based on these five plots, can we fit a regression line in each case? Justify your answer.
  • For those plots where a regression line is meaningful, fit the regression line and construct at least three meaningful residual plots for each of the lines you have fitted.
  • Use your lines to make the following predictions of calories, using 2.5, 4, and 15 for fat; 5, 12.5, and 50 for sugars; 100, 250, and 500 for potassium; 25, 60, and 120 for vitamins; and 5, 30, 70, for rating. Are all of these meaningful predictions? Be specific and use the proper statistical terms.
  • Carefully assess your residual plots. Do these plots suggest that your fitted regression lines is suitable to describe the relationship? Be specific and indicate which of the residual plots suggest that your fitted regression line is meaningful and which residual plots are not very informative.
  • Provide an overall assessment how the five variables affect calories in cereals. Which variables seem to have a strong effect on calories and which variables seem to have a minor (possibly neglectable) effect? Think carefully about the relationship between calories and rating!
  • Write a computer-based conclusive report of your results (a total of four to five pages, including all figures). Look at the solutions of HW 2, Exercise 4, how to structure such a report. Just the computer output will result in at most 50% of the possible points for this exercise.