Solution Found!
SAT, take 2 Suppose we wanted to use SAT math scores to
Chapter 6, Problem 55E(choose chapter or problem)
Problem 55E
SAT, take 2 Suppose we wanted to use SAT math scores to estimate verbal scores based on the information in Exercise 53.
a) What is the correlation?
b) Write the equation of the line of regression predicting verbal scores from math scores.
c) In general, what would a positive residual mean in this context?
d) A person tells you her math score was 500. Predict her verbal score.
e) Using that predicted verbal score and the equation you created in Exercise 53, predict her math score.
f) Why doesn’t the result in part e come out to 500?
Exercise 53:
SAT scores The SAT is a test often used as part of an application to college. SAT scores are between 200 and 800, but have no units. Tests are given in both Math and Verbal areas. SAT-Math problems require the ability to read and understand the questions, but can a person’s verbal score be used to predict the math score? Verbal and math SAT scores of a high school graduating class are displayed in the scatterplot, with the regression line added.
a) Describe the relationship.
b) Are there any students whose scores do not seem to fit the overall pattern?
c) For these data, r = 0.685. Interpret this statistic.
d) These verbal scores averaged 596.3, with a standard deviation of 99.5, and the math scores averaged 612.2, with a standard deviation of 96.1. Write the equation of the regression line.
e) Interpret the slope of this line.
f) Predict the math score of a student with a verbal score of 500.
g) Every year, some students score a perfect 1600. Based on this model, what would such a student’s residual be for her math score?
Questions & Answers
QUESTION:
Problem 55E
SAT, take 2 Suppose we wanted to use SAT math scores to estimate verbal scores based on the information in Exercise 53.
a) What is the correlation?
b) Write the equation of the line of regression predicting verbal scores from math scores.
c) In general, what would a positive residual mean in this context?
d) A person tells you her math score was 500. Predict her verbal score.
e) Using that predicted verbal score and the equation you created in Exercise 53, predict her math score.
f) Why doesn’t the result in part e come out to 500?
Exercise 53:
SAT scores The SAT is a test often used as part of an application to college. SAT scores are between 200 and 800, but have no units. Tests are given in both Math and Verbal areas. SAT-Math problems require the ability to read and understand the questions, but can a person’s verbal score be used to predict the math score? Verbal and math SAT scores of a high school graduating class are displayed in the scatterplot, with the regression line added.
a) Describe the relationship.
b) Are there any students whose scores do not seem to fit the overall pattern?
c) For these data, r = 0.685. Interpret this statistic.
d) These verbal scores averaged 596.3, with a standard deviation of 99.5, and the math scores averaged 612.2, with a standard deviation of 96.1. Write the equation of the regression line.
e) Interpret the slope of this line.
f) Predict the math score of a student with a verbal score of 500.
g) Every year, some students score a perfect 1600. Based on this model, what would such a student’s residual be for her math score?
ANSWER:
Step 1 of 6
The coefficients of the linear regression line are
(a) 0.685