Question #24 / 25 In ongoing economic analyses, the U.S. federal government comp
ID: 3063834 • Letter: Q
Question
Question #24 / 25 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 y2.74 +2.49x 1980 per capita income, x 1999 per capita income, Y Ohio Vermont Florida New York 38 36 34 32 30 28 10.1 8.7 10.0 11.1 7.1 10.2 10.4 8.2 11.2 8.1 11.1 9.7 8.4 12.0 27.1 25.9 28.0 33.9 20.5 27.1 27.8 23.2 32.2 23.5 31.3 25.7 22.1 29.8 Michigan Kentucky Maryland North Dakota 24 20 owa New Mexico California Figure 1 Based on the above information, answer the following: per cap greater than the mean of the 1999 per capita incomes tend to be paired with 1980 per capita incomes that are Choose one the mean of the 2. According to the regression equation, for an increase of one thousand dollars in 1980 per capita income, there is a corresponding increase of how many thousand dollars in 1999 per capita income? 3. What was the observed 1999 per capita income (in thousands of dollars) when the 1980 per capita income was 10.1 thousand dollars? 4. From the regression equation, what is the predicted 1999 per capita income (in thousands of dollars) when the 1980 per capita income is 10.1 thousand dollars? (Round your answer to at least one decimal place.) Clear Undo HeExplanation / Answer
1)By Observation,For these data, 1999 per capita incomes that are greater than the mean of the 1999 per capita incomes tend to be paired with 1980 per capita incomes that are geater than the 1980.
2) According to the regression equation, for an increase of one thousand dollars in 1980 per capita income,there is a corresponding increase is 5.23 thousand dollars in 1999 per capita income.
because,
y^ = 2.74+2.49 * x
y^ = 2.74+2.49 * 1
y^ = 5.23
3)When the 1980 per capita income is 10.1 thousand dollars, The observed 1999 per capita income 27.89 thousand dollars.
y^ = 2.74+2.49 * x
y^ = 2.74+2.49 * 10.1
y^ = 27.89
4)When the 1980 per capita income is 10.1 thousand dollars, The observed 1999 per capita income 27.9 thousand dollars.
y^ = 2.74+2.49 * x
y^ = 2.74+2.49 * 10.1
y^ = 27.9