mber of cars in se 2 Regression to the mean (15 points) We expect that students

Question

mber of cars in se 2 Regression to the mean (15 points) We expect that students w on the final exam. Gary Smith of Pomona College looked at the exam scores of all 1000 students who took his statistics class over a 15-year period. The least-squares line for predicting final-exam score from midterm-exon score was, = 52.5 + 0.34x. (Both exams have a 100-poit scale.) Joana scores 8 points above the class mean on the midterm How many points above the class mean do you predict that he will score on the final? (Hint: use the fact that the least squares passes through the point , y) and the fact that Joana's midterm score is 8.) (10 points each.)

Explanation / Answer

Q.2 As the hint is given in the question. Linear regression line is given which is

y^ = 52.5 + 0.34x

so lets say mean of the midterm paper is x and mean of the final paper is

so this point (x, ) will lie on the regression line.

= 52.5 + 0.34 x

so if joanna scoring marke  x + 8 in midterm paper so predictive score of her in the final paper is

y^ = 52.5 + 0.34 (x + 8) = 52.5 + 0.34x + 2.72

y^ = + 2.72

so she will score 2.72 more marks in final paper than the final paper mean.

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