A STAT 200 instructor believes that the average quiz score is a good predictor o
ID: 3056206 • Letter: A
Question
A STAT 200 instructor believes that the average quiz score is a good predictor of final exam score. A random sample of 8 students produced the following data where x is the average quiz score and y is the final exam score.
x 85 50 72 65 78 60 100 70
y 85 75 75 64 80 65 95 60
(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 exam score if the average quiz score is 80? Show all work and justify your answer.
Explanation / Answer
a)
b1= nE(xy)-ExEy/nE(x2)-(Ex2)
= 8*44375-580*599/8*43718-(580)^2
= 0.5680
b0=Ey-b1Ex/n
=599-(0.5680*580)/8
=33.69
y=b0+b1x
=33.69+0.5680x
b)
33.69+0.5680*80
79.1353
x y x^2 y^2 xy 85 85 7225 7225 7225 50 75 2500 5625 3750 72 75 5184 5625 5400 65 64 4225 4096 4160 78 80 6084 6400 6240 60 65 3600 4225 3900 100 95 10000 9025 9500 70 60 4900 3600 4200 Ex Ey Ex^2 Ey^2 Exy 580 599 43718 45821 44375Related Questions
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