A STAT 200 instructor believes that the average quiz score is a good predictor o
ID: 3289565 • Letter: A
Question
A STAT 200 instructor believes that the average quiz score is a good predictor of final test score. A random sample of 10 students produced the following data where x is the average quiz score and y is the final test score.
x
80
93
50
60
100
40
85
70
75
85
y
70
96
50
70
96
38
83
65
77
87
(a) Find an equation of the least squares regression line. Show all work; writing the correct equation, without supporting work, will receive no credit.
(b) Based on the equation from part (a), what is the predicted final test score if the average quiz score is 90? Show all work and justify your answer.
x
80
93
50
60
100
40
85
70
75
85
y
70
96
50
70
96
38
83
65
77
87
Explanation / Answer
Ans:
a) For linear regression:
Regression Equation(y) = a + bx
Slope(b) = (NXY - (X)(Y)) / (NX2 - (X)2)
Intercept(a) = (Y - b(X)) / N
First calculate above terms from given data as:
Slope,b=(10*57123-738*732)/(10*57724-(738)2 )=0.95147
y-Intercept,a=(732-0.95147*738)/10=2.98178
Hence,regression line is
y=2.982+0.951x
(y is perdicted value for any x)
b) if x=90
y=2.982+0.951*90=88.572
y=88.572
hence ,for average quiz score=90,perdicted final test score=88.572
x y xy x^2 y^2 1 80 70 5600 6400 4900 2 93 96 8928 8649 9216 3 50 50 2500 2500 2500 4 60 70 4200 3600 4900 5 100 96 9600 10000 9216 6 40 38 1520 1600 1444 7 85 83 7055 7225 6889 8 70 65 4550 4900 4225 9 75 77 5775 5625 5929 10 85 87 7395 7225 7569 Total 738 732 57123 57724 56788