An instructor believes that the average quiz score is a good predictor of final

Question

An instructor believes that the average quiz score is a good predictor of final exam score. A random sample of 10 students produced the following data where x is the average quiz score and y is the final exam score
x 80 93 50 60 100 40 85 70 75 85

y 72 95 75 68   90 35 83 60 77 85

(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 90? Show all work and justify your answer.

Explanation / Answer

Line of Regression Y on X i.e Y = bo + b1 X

Mean of X = X / n =    73.8
Mean of Y = Y / n =   74
(Xi - Mean)^2 =   3259.6
(Yi - Mean)^2 =   2666
(Xi-Mean)*(Yi-Mean) =   2468
b1 = (Xi-Mean)*(Yi-Mean) / (Xi - Mean)^2    
b1 = 2468 / 3259.6 = 0.75715  
bo = Y / n - b1 * X / n  
bo = 74 - 0.75715*73.8 = 18.12247  
  
Y = bo + b1 X  
  
Y'=18.12247+0.75715*X  

b.

the predicted final exam score if the average quiz score is 90

Y'=18.12247+0.75715*(90) = 86.26597

X Y (Xi - Mean)^2 (Yi - Mean)^2 (Xi-Mean)*(Yi-Mean) 80 72 38.44 4 -12.4 93 95 368.64 441 403.2 50 75 566.44 1 -23.8 60 68 190.44 36 82.8 100 90 686.44 256 419.2 40 35 1142.44 1521 1318.2 85 83 125.44 81 100.8 70 60 14.44 196 53.2 75 77 1.44 9 3.6 85 85 125.44 121 123.2

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