Question

1. The following lists midterm and final exam grades for randomly selected students:

Midterm (x) 82 65 93 70 85 50 95 80

Final (y) 94 77 94 79 95 70 97 91

a). Plot the scatter diagram.

b). find the value of the linear correlation coefficient r.

c). find the equation of the regression line that best fits the data.

d). If you received a 76 on the midterm, what grade could you expect on the final?

e). If a student receives a 90 on his final, what would you expect he would have scored on his midterm?

Answer 1

From above information

a.

b.

Correlation coefficient that indicates the strength of the relationship between two variables can be found using the following formula:

Where:

• rxy – the correlation coefficient of the linear relationship between the variables x and y
• xi – the values of the x-variable in a sample
• x̅ – the mean of the values of the x-variable
• yi – the values of the y-variable in a sample
• ȳ – the mean of the values of the y-variable

Hence, rxy=0.960 , strong correlation

c.

Regression equation,

Final(Y)=36.81+0.64 Midterm(X)

d.

If we received a 76 on the midterm the grade could you expect on the final X=76 is

Final(Y)=85.45

e.

If a student receives a 90 on his final means Y=90, then scored on his Midterm is

X(Midterm)=83.10

Thanks ,dear

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