Variable Selection:

Place discussion of the best explanatory variable here

Model:

We wish to model the relationship between starting income, measured in dollars, and grade point average (GPA) for a population of recent non-computer science graduates (class of 1996). Let y denote starting income and x GPA, then the simple linear regression model for this problem is:

where, for each x_i, e_ij is assumed to:

• be normally distributed
• have the same standard deviation
• have mean zero

Discussion:

From the SAS Analysis of Variance report, the parameter estimates are:

a = 271.54
b = 7994.98
s_y|x = 2239.25

Hence, the regression equation is y=271.54 + 7994.98x which indicates that for unit increase in GPA we can expect an increase in starting income of about $7995. Also, the equation indicates that we can expect a starting income of $271.54 for a GPA of zero. Since the minimum observed GPA is 1.6 this interpretation is probably not meaningful.

The r-square value of 0.8677 indicates that about 87% of the variability in starting income is explained by the regression model. Since the model is a simple linear regression model we can also conclude that the correlation coefficient is +sqrt(0.8667) (i.e. 0.931) indicating strong positive correlation between starting income and GPA.

If necessary, place solutions to worked problems here

Extra Credit Section:

To assess the normality assumption we conducted a normality test of the residuals. Hypotheses for testing the normality assumption are:

H₀: Residuals are drawn from a normal distribution
H_a: Residuals are not drawn from a normal distribution

The p-value is 0.6960 indicating that we have insufficient reason to doubt the null-hypothesis and so the normality assumption is reasonable.

If necessary, place solutions to extra credit problems here