Assignment 8, Fall 2000

STATISTICS 403 - Assignment 8

Due Thursday, November 30, 2000

Below are the scores for eleven women golfers for a tournament that consisted of two rounds of golf.
```
Golfer     |  1    2    3    4    5    6     7    8    9   10   11
-------------------------------------------------------------------
Round 1, X | 89   90   87   95   86   81   115   83   88   91   79
Round 2, Y | 94   85   89   89   81   76    89   87   91   88   80
-------------------------------------------------------------------
```
- (a) Compute Kendall's T for these data.
- (b) Is the value in (a) statistically significant?
- (c) Compute Kendall's T for the ten golfers excluding golfer #7.
- (d) Is the value in (c) statistically significant?
- (e) The linear regression equation that predicts Round 2 score, Y, from the Round 1 score, X (using all 11 golfers) is: Y = 63.6 + 0.254X Use this equation to predict the second round score for golfer #7. What is the associated residual?
- (f) Develop a rank regression equation that predicts the rank of Y from the rank of X. Again use all 11 golfers.
- (g) Use the rank regression equation in (f) to come up with a predicted Round 2 score for golfer #7. What is the associated residual?
- (h) Which gives a better prediction of golfer #7's second round score? Support your answer by referring to the residuals.
In an attempt to relate the age (in years), X, of a foreign subcompact car and that car's asking price (in \$100), Y, six used cars of different ages are taken and information on asking price is obtained. The data are given below.
```
Age (years)      3    4    5    6    7    8
--------------------------------------------
Price ($100)    54   48   45   33   35   31
```
- (a) Plot the data. What is the apparent relationship between Age and Price?
- (b) Pearson's Correlation Coefficient, r = -0.952 with a one sided P-value = 0.0015. What do these values say about the strength of the relationship between Age and Price?
- (c) Calculate Kendall's Correlation Coefficient, T and the associated P-value. What do these values say about the strength of the relationship between Age and Price?
- (d) Using simple linear regression the equation that predicts Price, Y, from Age, X, Y = 67.1 - 4.74X Use this euation to predict the Price for a foreign subcompact that is 7 years old. Compute the residual for this prediction.
- (e) Use Theil's method to come up with a linear prediction equation that predicts Price from Age.
- (f) Use the equation in (e) to predict the Price for a foreign subcompact that is 7 years old. Compute the residual for this prediction.
- (g) Which method, simple linear regression or Theil's method, produces a better prediction of the asking price for a foreign subcompact that is 7 years old? Support your answer by referring to the residuals.