An educational researcher was interested in the effect of academic performance in high school on academic performance in college. She consulted the school records of 12 college graduates, all of whom had attended the same high school, to determine their high school cumulative grade average (X) and their cumulative grade average in college (Y). The following results were obtained:
X Y
3.3………………………………. 2.7
2.9………………………………. 2.5
2.5………………………………. 1.9
4.0………………………………. 3.3
2.8………………………………. 2.7
2.5………………………………. 2.2
3.7………………………………. 3.1
3.8………………………………. 4.0
3.5………………………………. 2.9
2.7………………………………. 2.0
2.6………………………………. 3.1
4.0………………………………. 3.2
a. Draw a scatter plot of the data.
b. Calculate the regression slope and Y-intercept.
c. Draw the regression line on the scatter plot.
d. Predict the college grade average of a student who attains a 3.0 grade average in high school.
e. Find the coefficients of determination and nondetermination. What do they mean?