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In ongoing economic analyses, the U.S. federal government compares per capita incomes not only among different states but also for the same state at different times. Typically, what the federal government finds is that "poor" states tend to stay poor and "wealthy" states tend to stay wealthy. Would we have been able to predict the 1999 per capita income for a state (denoted by y) from its 1980 per capita income (denoted by x)? The following bivariate data give the per capita income (in thousands of dollars) for a sample of fourteen states in the years 1980 and 1999 (source: U.S. Bureau of Economic Analysis, Survey of Current Business, May 2000). The data are plotted in the scatter plot in Figure 1, and the least-squares regression line is drawn. The equation for this line is y = 3.09+2.47x. 1980 per capita 1999 per capita income, y (in $1000s) income, x (in $1000s) Vermont 8.7 25.9 38- Hawaii 11.5 27.8 36- Missouri 9.4 26.2 34- Nebraska Kansas 9.3 27.4 32- 10.0 26.6 30- North Dakota Delaware South Carolina New Jersey 8.1 23.5 28- 10.8 30.7 26- 7.8 23.5 24 11.8 36.1 Utah Arizona 8.5 23.4 9.6 25.3 Montana 9.1 22.3 Maine 8.4 25.0 Illinois 11.1 31.3 Figure 1 Send data to Excel

In ongoing economic analyses, the U.S. federal government compares per capita incomes not only among different states but also for the same state at different times. Typically, what the federal government finds is that "poor" states tend to stay poor and "wealthy" states tend to stay wealthy. Would we have been able to predict the 1999 per capita income for a state (denoted by y) from its 1980 per capita income (denoted by x)? The following bivariate data give the per capita income (in thousands of dollars) for a sample of fourteen states in the years 1980 and 1999 (source: U.S. Bureau of Economic Analysis, Survey of Current Business, May 2000). The data are plotted in the scatter plot in Figure 1, and the least-squares regression line is drawn. The equation for this line is y = 3.09+2.47x. 1980 per capita 1999 per capita income, y (in $1000s) income, x (in $1000s) Vermont 8.7 25.9 38- Hawaii 11.5 27.8 36- Missouri 9.4 26.2 34- Nebraska Kansas 9.3 27.4 32- 10.0 26.6 30- North Dakota Delaware South Carolina New Jersey 8.1 23.5 28- 10.8 30.7 26- 7.8 23.5 24 11.8 36.1 Utah Arizona 8.5 23.4 9.6 25.3 Montana 9.1 22.3 Maine 8.4 25.0 Illinois 11.1 31.3 Figure 1 Send data to Excel

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 22EQ
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O REGRESSION AND CORRELATION 三I Predictions from the least-squares regression line Shas In ongoing economic analyses, the U.S. federal government compares per capita incomes not only among different states but also for the same state at different times. Typically, what the federal government finds is that "poor" states tend to stay poor and "wealthy" states tend to stay wealthy. Would we have been able to predict the 1999 per capita income for a state (denoted by y) from its 1980 per capita income (denoted by x)? The following bivariate data give the per capita income (in thousands of dollars) for a sample of fourteen states in the years 1980 and 1999 (source: U.S. Bureau of Economic Analysis, Survey of Current Business, May 2000). The data are plotted in the scatter plot in Figure 1, and the least-squares regression line is drawn. The equation for this line is y = 3.09+2.47x. 1980 per capita 1999 per capita income, x (in $1000s) income, y (in $1000s) Vermont 38+ 8.7 25.9 Hawaii 11.5 27.8 36+ Missouri 9.4 26.2 34+ Nebraska 9.3 27.4 32+ Kansas 10.0 26.6 30+ North Dakota 8.1 23.5 28+ Delaware 10.8 30.7 26+ South Carolina 7.8 23.5 24- New Jersey Utah 11.8 36.1 8.5 23.4 22 Arizona 9.6 25.3 20- Montana 9.1 22.3 Maine 8.4 25.0 Illinois 11.1 31.3 Figure 1 Send data to Excel Explanation Check O 2021 McGraw-Hill Education. All Rights Reserved Terms of Use Privacy Acce ype here to search O
Transcribed Image Text:O REGRESSION AND CORRELATION 三I Predictions from the least-squares regression line Shas In ongoing economic analyses, the U.S. federal government compares per capita incomes not only among different states but also for the same state at different times. Typically, what the federal government finds is that "poor" states tend to stay poor and "wealthy" states tend to stay wealthy. Would we have been able to predict the 1999 per capita income for a state (denoted by y) from its 1980 per capita income (denoted by x)? The following bivariate data give the per capita income (in thousands of dollars) for a sample of fourteen states in the years 1980 and 1999 (source: U.S. Bureau of Economic Analysis, Survey of Current Business, May 2000). The data are plotted in the scatter plot in Figure 1, and the least-squares regression line is drawn. The equation for this line is y = 3.09+2.47x. 1980 per capita 1999 per capita income, x (in $1000s) income, y (in $1000s) Vermont 38+ 8.7 25.9 Hawaii 11.5 27.8 36+ Missouri 9.4 26.2 34+ Nebraska 9.3 27.4 32+ Kansas 10.0 26.6 30+ North Dakota 8.1 23.5 28+ Delaware 10.8 30.7 26+ South Carolina 7.8 23.5 24- New Jersey Utah 11.8 36.1 8.5 23.4 22 Arizona 9.6 25.3 20- Montana 9.1 22.3 Maine 8.4 25.0 Illinois 11.1 31.3 Figure 1 Send data to Excel Explanation Check O 2021 McGraw-Hill Education. All Rights Reserved Terms of Use Privacy Acce ype here to search O
1. Fill in the blank: For these data, 1999 per capita incomes that are greater than the mean of the 1999 per capita incomes tend to be Choose one paired with 1980 per capita incomes that are the mean of the 1980 per capita incomes. 2. Fill in the blank: According to the regression equation, for an increase of one thousand dollars in 1980 per capita income, there is a Choose one corresponding of 2.47 thousand dollars in 1999 per capita income. 3. From the regression equation, what is the predicted 1999 per capita income (in thousands of dollars) when the 1980 per capita income is 10.2 thousand dollars? (Round your answer to at least one decimal place.) 4. From the regression equation, what is the predicted 1999 per capita income (in thousands of dollars) when the 1980 per capita income is 10.8 thousand dollars? (Round your answer to at least one decimal place.)
Transcribed Image Text:1. Fill in the blank: For these data, 1999 per capita incomes that are greater than the mean of the 1999 per capita incomes tend to be Choose one paired with 1980 per capita incomes that are the mean of the 1980 per capita incomes. 2. Fill in the blank: According to the regression equation, for an increase of one thousand dollars in 1980 per capita income, there is a Choose one corresponding of 2.47 thousand dollars in 1999 per capita income. 3. From the regression equation, what is the predicted 1999 per capita income (in thousands of dollars) when the 1980 per capita income is 10.2 thousand dollars? (Round your answer to at least one decimal place.) 4. From the regression equation, what is the predicted 1999 per capita income (in thousands of dollars) when the 1980 per capita income is 10.8 thousand dollars? (Round your answer to at least one decimal place.)
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