A study was conducted to determine whether the final grade of a student in an introductory psychology course is linearly related to his or her performance on the verbal ability test administered before college entrance.

The verbal scores and final grades for 10 students are shown.

Student Verbal Score x=78,56,66,53,68,71,30.27,46,46
Final Grade Y= 87,67,80,73,99,84,74,72,61,80

Find the following:

a. The correlation coefficient: r=
b. The least squares line: y^=
c. Calculate the residual for the ninth student:

a) In order to calculate the correlation coefficient we can use this formula:  

And replacing we got:

b)  

And the slope would be:  

Nowe we can find the means for x and y like this:  

And we can find the intercept using this:  

So the line would be given by:  

c) For this case if we use the score for the 9th student we got:

And the residual is given by:

Step-by-step explanation:

Part a

In order to calculate the correlation coefficient we can use this formula:  

And replacing we got:

Part b

We need to find a model like this one:

Where:  

With these we can find the sums:  

And the slope would be:  

Nowe we can find the means for x and y like this:  

And we can find the intercept using this:  

So the line would be given by:  

Part c

For this case if we use the score for the 9th student we got:

And the residual is given by:

72 is the answer to this problem