For a sample of 306 students in a basic business statistics course, the sample regression line
y = 58.813 + 0.2875x
was obtained. Here,
y = final student score at the end of the course
x = score on a diagnostic statistics 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 the population regression line was 0.04566.
a. Interpret the slope of the sample regression line.
b. Interpret the coefficient of determination.
c. The information given allows the null hypothesis that the slope of the population regression line is 0 to be tested in two different ways against the alternative that it is positive. Carry out these tests and show that they reach the same conclusion.