Question

10.30  Grade inflation. The average undergraduate GPA for American colleges and universities was estimated based on a sample of institutions that published this information.¹³ Here are the data for public schools in that report:

Year	1992	1996	2002	2007
GPA	2.85	2.90	2.97	3.01

Do the following by hand or with a calculator and verify your results with a software package.

1. (a) Make a scatterplot that shows the increase in GPA over time. Does a linear increase appear reasonable?

2. (b) Find the equation of the least-squares regression line for predicting GPA from year. Add this line to your scatterplot.

3. (c) Compute a 95% confidence interval for the slope and summarize what this interval tells you about the increase in GPA over time.

Answer 1

YES LINEAR INCREASE APPEAR REASONABLE.

SOLUTION B:

Based on the above table, the following is calculated:

Therefore, based on the above calculations, the regression coefficients (the slope m, and the y-intercept n) are obtained as follows:

GPA=−18.5891+0.0108YEAR

SOLUTION C: To compute 95% confidence interval for slope we need to find out estimated standard error of estimate for slope

SE = sm = sqrt [ Σ(y_i - ŷ_i)² / (n - 2) ] / sqrt [ Σ(x_i - x)² ]

= sqrt[0.000123518/4]/sqrt(130.75)

= 0.007858695/11.43459663

= 0.000687

t critical value= 4.3

95% confidence interval is