Q1 The number of pass attempts and passing yards for seven professional quarterbacks for a recent regular season is given.

Question

Pass Attempts, x           583      571      550      541      506      514      486

Passing Yards, y             4770     4500     4483     4434     4328     4388     4254

a)    Calculate the sample correlation coefficient and identify the type of correlation 

that exists if any.

b)    What interpretation can you conclude from the given data?

c)    Is the relationship significant? Explain.

e)    Determine the equation of the regression line.

f)     Use the regression line to predict the number of passing yards for a quarterback who had 530   passing attempts.

.

Answer 1

Using two different linear regression calculators, the equations of the best fit trend line is:

y=4.24427727x + 2,176.67371 (e)

with R-Coefficient 0.91170513 (a)

So the data fits a linear model quite well (c)

That means for every pass attempt, the # of yards increases by 4.24427727;

the average pass completion is almost 4 and 1/4 yards; Therefore, the QB

gains 2,176.67371 RUSHING yards per season: about 2176/16 = 136 rushing yards per game

4.24427727* 530 + 2176.67371 = 4,431.9706631 or, 4432 yards for 530 attempts