Suppose John is a high school statistics teacher who believes that watching many hours of TV leads to lower test scores. Immediately after giving the most recent test, he surveyed each of the 24 students in his class and asked them how many hours of TV they watched that week. He then matched each student's test grade with his or her survey response. After compiling the data, he used hours of TV watched to predict each student's test score. He found the least-squares regression line to be ŷ = -1.5x + 85. He also calculated that the value of r, the correlation coefficient, was –0.61. Which of the choices identifies the correct value of the coefficient of determination, R², and gives a correct interpretation of its meaning? O R? = 0.61, meaning 61% of the total variation in hours of TV watched can be explained by the least-squares regression line. R = 0.3721, meaning 37.21% of the total variation in test scores can be explained by the least-squares regression line. O R? = 0.3721, meaning 37.21% of the total variation in hours of TV watched can be explained by the least-squares regression line. R = 0.61, meaning 61% of the total variation in test scores can be explained by the least-squares regression line. O R? = 0.781, meaning 78.1% of the total variation in test scores can be explained by the least-squares regression line.
Suppose John is a high school statistics teacher who believes that watching many hours of TV leads to lower test scores. Immediately after giving the most recent test, he surveyed each of the 24 students in his class and asked them how many hours of TV they watched that week. He then matched each student's test grade with his or her survey response. After compiling the data, he used hours of TV watched to predict each student's test score. He found the least-squares regression line to be ŷ = -1.5x + 85. He also calculated that the value of r, the correlation coefficient, was –0.61. Which of the choices identifies the correct value of the coefficient of determination, R², and gives a correct interpretation of its meaning? O R? = 0.61, meaning 61% of the total variation in hours of TV watched can be explained by the least-squares regression line. R = 0.3721, meaning 37.21% of the total variation in test scores can be explained by the least-squares regression line. O R? = 0.3721, meaning 37.21% of the total variation in hours of TV watched can be explained by the least-squares regression line. R = 0.61, meaning 61% of the total variation in test scores can be explained by the least-squares regression line. O R? = 0.781, meaning 78.1% of the total variation in test scores can be explained by the least-squares regression line.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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Question
Suppose John is a high school statistics teacher who believes that watching many hours of TV leads to lower test scores. Immediately after giving the most recent test, he surveyed each of the 24 students in his class and asked them how many hours of TV they watched that week. He then matched each student's test grade with his or her survey response. After compiling the data, he used hours of TV watched to predict each student's test score. He found the least-squares regression line to be ?̂ =−1.5?+85y^=−1.5x+85. He also calculated that the value of ?r, the correlation coefficient , was −0.61.
Which of the choices identifies the correct value of the coefficient of determination, ?2R2, and gives a correct interpretation of its meaning?
Transcribed Image Text:Suppose John is a high school statistics teacher who believes that watching many hours of TV leads to lower test scores.
Immediately after giving the most recent test, he surveyed each of the 24 students in his class and asked them how many hours
of TV they watched that week. He then matched each student's test grade with his or her survey response. After compiling the
data, he used hours of TV watched to predict each student's test score. He found the least-squares regression line to be
ŷ = -1.5x + 85. He also calculated that the value of r, the correlation coefficient, was -0.61.
Which of the choices identifies the correct value of the coefficient of determination, R², and gives a correct interpretation of
its meaning?
R = 0.61, meaning 61% of the total variation in hours of TV watched can be explained by the least-squares
regression line.
R = 0.3721, meaning 37.21% of the total variation in test scores can be explained by the least-squares regression line.
R = 0.3721, meaning 37.21% of the total variation in hours of TV watched can be explained by the least-squares
regression line.
R = 0.61, meaning 61% of the total variation in test scores can be explained by the least-squares regression line.
O R?
0.781, meaning 78.1% of the total variation in test scores can be explained by the least-squares regression line.
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