The following set of 25 scores was randomly selected from a teacher€™s class list. Let x be the pre-final average and y be the final examination score. (The final examination had a maximum of 75 points.)

a. Draw a scatter diagram for these data.
b. Draw the regression line (by eye) and estimate its equation.
c. Estimate the value of the coefficient of linear correlation.
d. Calculate the equation of the line of best fit.
e. Draw the line of best fit on your graph. How does it compare with your estimate?
f. Calculate the linear correlation coefficient. How does it compare with your estimate?
g. Test the significance of r at a = 0.10.
h. Find the 95% confidence interval for the true value of r.
i. Find the standard deviation of the y values about the regression line.
j. Calculate a 95% confidence interval for the true value of the slope b1.
k. Test the significance of the slope at a = 0.05 .
l. Estimate the mean final exam grade that all students with an 85 prefinal average will obtain (95% confidence interval).
m. Using the 95% prediction interval, predict the grade that John Henry will receive on his final, knowing that his prefinal average is 78.

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