Problem Set 3

1. Ten of the many college seniors who took the LSAT exam twice were drawn at random. Their scores are shown below:

                student      1st  2nd
                -----------------------------
                 Able        30   30
                 Black       25   27
                 Costello    25   25
                 Donner      29   26
                 Efrom       26   28
                 Fari        27   27
                 Guest       23   24
                 Henry       28   31
                 Inman       26   23
                 Jason       31   29 

   1. Do a scatterplot of the ten points, treating the first try as X and the second try as Y.
   2. Eyeball estimate b₁ from the plot.
   3. Calculate the least squares regression line.
   4. Calculate r.
   5. Obtain the 95% interval estimate of ß₀, ß₁.
   6. Test the null hypothesis of no relationship between exam scores for two attempts at the exam:
   1. Based on b₁.
   2. Based on r.
   
   
   
2. Do a regression analysis on the following data:

             Y     X
            4.2    1 
            5.1    1 
            3.8    2 
            6.3    2 
            2.9    3 
            5.4    3 
            7.3    3 
            2.8    4 
            6.5    4 
            9.1    4        

   1. Graphically examine the results for evidence of heteroscedasticity, and do both a Modified Levene Test and a Breusch-Pagan Test.
   2. Graphically examine the results for evidence of non-normality of the error terms, including an appropriate statistical test..

    

3. You are an analyst in the Department of Revenue. You suspect that there is a pattern in the receipt of income tax payments between January 1 and April 15. You obtain the following weekly data:

        Week     Receipts 
        1           101      
        2           132      
        3           149      
        4           108
        5            91      
        6            90      
        7            63      
        8            39      
        9            58      
        10           88 
        11           99 
        12          126 
        13          134 
        14          159 
        15          177 

   1. Using Week as the predictor, and Receipts as the dependent variable, examine the above data for nonlinearity.
   2. Identify an appropriate transformation and estimate the regression equation. (Caution: do not just through the variables into Box-Cox; consider what form of a relationship is suggested by the scatterplot.)

    

4. Do projects 2.62 and 3.25 in Kutner.

Bert Kritzer, 608-263-2277, Kritzer@PoliSci.Wisc.Edu
Last modified, February 26, 2004