Since 1982, the year that PGA Tour officials began tracking charitable donations from its tournaments on an annual basis, no event has contributed more to charities in its community than the Byron Nelson tournament. The amount donated each year from 1982 through 2002 (in millions of dollars) isdown below:

This is the data set for the question:

Year Donation

1982 0.85

1983 1.20

1984 1.34

1985 1.54

1986 1.52

1987 1.61

1988 2.04

1989 1.74

1990 2.39

1991 2.64

1992 3.05

1993 3.63

1994 3.20

1995 3.35

1996 3.83

1997 4.35

1998 4.35

1999 5.92

2000 6.10

2001 6.10

2002 5.77

a. Fit a simple linear trend model with DONATION as the response and YEAR as the explanatory variable. State the equation of this fitted model using appropriate statistical notation.

b. For the model fit in part (a), assumptions 1 - 3 appear to be met, but there is evidence of positive autocorrelation indicating that assumption 4 (independence) is violated. To try to fix this, create lag variable for the response (DONATION) and refit the model. Your model will now have 2 explanatory variables; YEAR and LAGDONATION. State the equation of this fitted model using appropriate statistical notation.

c. Test whether adding the lag variable for the response fixed the issue with positive autocorrelation. For this, we will need test for positive autocorrelation for the model in part (b) at the 1% significance level by completing the following steps: i. State the null and alternative hypothesis ii. The test statistic for an test is = 1 (^2 ). Provide the values of r, n, and Sblag iii. Calculate the value of the an test statisics iv. State the cutoff value. v. Do you reject the null hypothesis or fail to reject the null hypothesis? Explain your answer. vi. Is there evidence of positive autocorrelation at the 1% significance level for the model in part (b)? (Yes or No is sufficient.)

d. For the model from part (b), characterize any unusual observations in this dataset. Be sure to state the cutoff values used as well as identify which years are potential unusual observations. Use ? = 0.05 when needed. Hint: be careful with your sample size, n

Cutoff Value (s) Year

Outliers - using standardized residuals

Outliers - using studentized residuals

Leverage points

Influential points - using DFITs

Influential points - using Cook's D