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 ») from its 1980 per capita income (denoted by )? 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 -3.09 + 2.47x. 1980 per capita 1999 per capita income, x (in $1000s) 8.7 income, y (in $1000s) Vermont 25.9 Hawail Missouri Nebraska 11.5 27.8 9.4 26.2 9.3 27.4 Kansas 10.0 26.6 North Dakota 8.1 23.5 Delaware South Carolina 10.8 30.7 7.8 23.5 New Jersey 11.8 36.1 Utah 8.5 23.4 Arizona 9.6 25.3 Montana Maine 9.1 22.3 8.4 25.0 Figure 1 Ilinois 11.1 31.3 Send data to Excel Based on the above information, answer the following: 1. Fil 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 corresponding income. Choose one of 2.47 thousand dolars in 1999 per capita 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.)

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 ») from its 1980 per capita income (denoted by )? 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 -3.09 + 2.47x. 1980 per capita 1999 per capita income, x (in $1000s) 8.7 income, y (in $1000s) Vermont 25.9 Hawail Missouri Nebraska 11.5 27.8 9.4 26.2 9.3 27.4 Kansas 10.0 26.6 North Dakota 8.1 23.5 Delaware South Carolina 10.8 30.7 7.8 23.5 New Jersey 11.8 36.1 Utah 8.5 23.4 Arizona 9.6 25.3 Montana Maine 9.1 22.3 8.4 25.0 Figure 1 Ilinois 11.1 31.3 Send data to Excel Based on the above information, answer the following: 1. Fil 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 corresponding income. Choose one of 2.47 thousand dolars in 1999 per capita 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.)

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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