For a sample of 306 students in a basic business communications course, the sample regression line

y = 58.813 + 0.2875xwas obtained. Here

y = final student score at the end of the course

x = score on a diagnostic writing skills test given at the beginning of the course

The coefficient of determination was 0.1158 and the estimated standard deviation of the estimator of the slope of population regression line was 0.04566.

a) Define and interpret the estimates of the regression equation.

b) Interpret the coefficient of determination.

c) What will happen to the final student score if his diagnostic writing test score increases by 2?

d) Test the null hypothesis that the slope of the population regression line is 0 against the alternative that the true slope is positive. Interpret your result. (Use 5% significance level)

e) How can you improve this model?