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Is the value of education worth its cost? Education costs are easy to calculate. They include tuition, books and living expenses as well as the cost of foregone income that a job would have provided. In an effort to learn more about the value of education, a university vice-president gathered data from a sample of 150 men and women (30 years old). Each was asked how many years of formal education he or she had completed (x) and his or her income (in $1000) for the previous 12 months (y). Summaries of a study conducted of n=150 people gave the following results (in $1000 s) : Ex=1976, Ey= 11719, SSxx=1657, SSyy=65247, SSxy=6857 a) Calculate the correlation coefficient (r) relating number of years of formal education and income. b) Find the regression line. c) Identify and interpret the slope in the context of the problem.

Is the value of education worth its cost? Education costs are easy to calculate. They include tuition, books and living expenses as well as the cost of foregone income that a job would have provided. In an effort to learn more about the value of education, a university vice-president gathered data from a sample of 150 men and women (30 years old). Each was asked how many years of formal education he or she had completed (x) and his or her income (in $1000) for the previous 12 months (y). Summaries of a study conducted of n=150 people gave the following results (in $1000 s) : Ex=1976, Ey= 11719, SSxx=1657, SSyy=65247, SSxy=6857 a) Calculate the correlation coefficient (r) relating number of years of formal education and income. b) Find the regression line. c) Identify and interpret the slope in the context of the problem.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.7: Applications
Problem 44EQ
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Question 1 Is the value of education worth its cost? Education costs are easy to calculate. They include tuition, books and living expenses as well as the cost of foregone income that a job would have provided. In an effort to learn more about the value of education, a university vice-president gathered data from a sample of 150 men and women (30 years old). Each was asked how many years of formal education he or she had completed (x) and his or her income (in $1000) for the previous 12 months (y). Summaries of a study conducted of n=150 people gave the following results (in $1000 s) Ex=1976, Ey= 11719, SSxx=1657, SSyy=65247, SSxy=6857 a) Calculate the correlation coefficient (r) relating number of years of formal education and income. b) Find the regression line. c) Identify and interpret the slope in the context of the problem. d) If a person had completed 12 years of formal education, what would you estimate the person's income to be? e) (i)If two variables have a correlation coefficient close to zero, it means there is no relationship between the two variables. True False (just circle the answer) (ii)R? measures how much of the variation in the response variable is explained by the linear relationship between the predictor and response. True False (just circle the answer)
Transcribed Image Text:Question 1 Is the value of education worth its cost? Education costs are easy to calculate. They include tuition, books and living expenses as well as the cost of foregone income that a job would have provided. In an effort to learn more about the value of education, a university vice-president gathered data from a sample of 150 men and women (30 years old). Each was asked how many years of formal education he or she had completed (x) and his or her income (in $1000) for the previous 12 months (y). Summaries of a study conducted of n=150 people gave the following results (in $1000 s) Ex=1976, Ey= 11719, SSxx=1657, SSyy=65247, SSxy=6857 a) Calculate the correlation coefficient (r) relating number of years of formal education and income. b) Find the regression line. c) Identify and interpret the slope in the context of the problem. d) If a person had completed 12 years of formal education, what would you estimate the person's income to be? e) (i)If two variables have a correlation coefficient close to zero, it means there is no relationship between the two variables. True False (just circle the answer) (ii)R? measures how much of the variation in the response variable is explained by the linear relationship between the predictor and response. True False (just circle the answer)
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