Regression to the mean
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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 College looked at the exam scores of all 346 students who took his statistics class over a 10-year period. *The least-squares line for predicting final exam score from midterm exam score was
y-hat = 46.6 + 0.41x. *
*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 exam?* (Hint: What is the predicted final score for the class mean midterm score x-bar?) This is an example of regression to the mean, the phenomenon that gave "regression" its name: students who do well on the midterm will on average do less well on the final, but still above the class mean.
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This solution explains how many points above a class mean should you predict a student will score on the final exam.
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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 College looked at the exam scores of all 346 students who took his statistics class over a 10-year period. *The least-squares line for predicting final exam score from midterm exam score was
y-hat = 46.6 + 0.41x. *
*Octavio scores 10 points ...
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- MA, Shandong Univ.
Recent Feedback
- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
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