Stat 250, Section 003, Homework Assignment 6 (Due 3/10/99 in class)

• 1) Look at "The Weather Page" from May 15, 1998 in USA Today. We took a random sample of 10 cities and got:
  
  Seattle (WA) 56/46
  Bismarck (ND) 73/47
  Richmond (VA) 83/57
  Raleigh (NC) 85/60
  Augusta (ME) 82/54
  Tulsa (OK) 85/62
  Tucson (AZ) 85/53
  Anchorage (AK) 53/42
  Denver (CO) 71/43
  Park City (UT) 54/31
  
  The first column indicates "forecast high", the second column is "tomorrow morning's low".
  
  • a) Draw a scatterplot of the data, plotting the "forecast high" on the (horizontal) x-axis and "tomorrow morning's low" on the (vertical) y-axis.
    
  • b) Describe the relationship you can see in the data.
    
  • c) Calculate SS(x), SS(y), SS(xy) for these 10 data points.
    
  • d) Determine the equation of the least squares line for this data.
    
  • e) Based on this equation, predict "tomorrow morning's lows" for given "forecast highs" of 60, 70, 85.
    
  • f) Would you use this equation to predict "tomorrow morning's low" for Nome (AK), knowing that the "forecast high" is 35? If so, which value do you get? And what is the predicted "tomorrow morning's low" according to USA Today? What happened?
  
  
• 2) Answer the two questions below. (2 points)
  
  
  
  
• 3) These questions are based on the scatterplot matrix presented in Mark Monmonier's article `Geographic Brushing: Enhancing Exploratory Analysis of the Scatterplot Matrix'. This scatterplot matrix has been reprinted below. (6 points)
  
  
  • Label the (individual) scatterplot that shows the `Cable Penetration' on the vertical (y-)axis and the `Per Capita Income' on the horizontal (x-)axis with the letter `A'.
  • What is the range R of the `Per Capita Income' (in $)?
  • Which of these statements is correct/incorrect?
    • The state with the highest `Per Capita Income' has a `Metropolitan Population' of less than 50%.
    • The state with the highest `Per Capita Income' has the second highest `Cable Penetration'.
    • Overall, there is a positive correlation (r > 0) between `Metropolitan Population' and `Per Capita Income'.
    • The 6 New England states have `Cable Penetrations' that range among the 15 lowest rates of cable penetration in the U.S.
    • California is the state with the highest `Per Capita Income'.
  
  
  
• 4) 10 students from Stat 250 wanted to determine the thickness of paper sheets used for the photocopying machines in S&T II. They grabbed a random number of sheets, counted the number of sheets, and measured the thickness of this pile of paper. Here is the data: (6 points)
  
  
  • Draw a scatterplot of Sheets (horizontal x-axis) and Thickness (vertical y-axis).
  • Fit a least squares (linear regression) line to the data. Make clear what your variables stand for. Also, add this line to your plot in above. It might help to know that:
    
    
  • What is a possible interpretation of the slope and y-intercept you calculated above? Isn't there something unexpected in the data?
  • Calculate Pearson's correlation coefficient r between x and y. How can we interpret this value for our given data set?
  • Based on your calculations above, what is the predicted thickness of 1 sheet, 100 sheets, 400 sheets, and 1,000 sheets. Which of these 4 predictions are more reliable, which are less reliable? Why?