Hi I need help with question number 48 in chapter 5. i couldn\'t answer it. the

Question

Hi
I need help with question number 48 in chapter 5. i couldn't answer it.
the question is "we expect that students who do well on the midterm exam in a course will usually also do well on the final exam. Gary smith of pomona collage looked at the exam scores of all 346 students who took his statistics class over a 10-year period. 17 the least squares line for predicting final exame score from midterm-exam score was ^y =46.6+0.41x ( both exams have a 100 point scale)
octavio scores 10 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 line passes through the point (x-,-y) and the fact that octavio's midterm is -x+10).this is another example of regression to the mean :student who do well on the midterm will on the average do less well, but still above average.

Explanation / Answer

To make the notation easier, let's write y_m as the mean score from the final exam, and x_m as the mean score for the midterm. Using the least squares line to relate them,

y_m = 46.6 + 0.41 x_m (this is the hint about the least squares line passing through the point (x_m, y_m))

Let's write Octavio's score for the midterm as x_o. Then from the least squares line his predicted final exam score y_o would be:

y_o = 46.6 + 0.41 x_o

We also know that he scored ten points above the mean on the midterm, in other words

x_o = x_m + 10

Putting this back into the equation for his final exam score:

y_o = 46.6 + 0.41 (x_m + 10) = 46.6 + 0.41 x_m + 4.1 = y_m + 4.1

So the least squares prediction is that he will score 4.1 points above the class mean on the final.

Related Questions

Navigate

• Browse (All)
• Browse H
• Subjects

---