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:

percentage - 25%

probability - 0.25

we know,

total amount of students in class = 20

total boys = 10

total girls = 10

no of girls who wear glasses = 10/2 = 5

probability of choosing a girl with glasses is =

number of girls wearing glasses/total number of students in the class = 5/20

thus, percentage of selecting a girl wearing glasses will be

= 5/20 × 100

= 5 × 5

25%

therefore,

probability will be 0.25

happy to

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