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+0.382.75x . 1980 per capita income, x(in $1000s)1999 per capita income, y(in $1000s)South Dakota8.125.1Utah8.523.4West Virginia8.220.9Arkansas7.622.1Kentucky8.223.2New Mexico8.422.1Ohio10.127.1Minnesota10.330.6Vermont8.725.9Alabama7.922.9Montana9.122.3Maryland11.232.2Iowa9.725.7Washington10.930.3 y20222426283032343638x78910111213 Figure 1 Based on the above information, answer the following: 1. Fill in the blank: For these data, 1999 per capita incomes that are less than the mean of the 1999 per capita incomes tend to be paired with 1980 per capita incomes that are _____ the mean of the 1980 per capita incomes.Choose onegreater thanless than2. 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 7.6 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 7.6 thousand dollars? (Round your answer to at least one decimal place.)

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Description: 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

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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

) 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

=y+0.382.75x

	1980 per capita income, x (in $1000s)	1999 per capita income, y (in $1000s)
South Dakota	8.1	25.1
Utah	8.5	23.4
West Virginia	8.2	20.9
Arkansas	7.6	22.1
Kentucky	8.2	23.2
New Mexico	8.4	22.1
Ohio	10.1	27.1
Minnesota	10.3	30.6
Vermont	8.7	25.9
Alabama	7.9	22.9
Montana	9.1	22.3
Maryland	11.2	32.2
Iowa	9.7	25.7
Washington	10.9	30.3

Figure 1

Based on the above information, answer the following:

1. Fill in the blank: For these data, 1999 per capita incomes that are less than the mean of the 1999 per capita incomes tend to be paired with 1980 per capita incomes that are _____ the mean of the 1980 per capita incomes.	Choose onegreater thanless than
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 7.6 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 7.6 thousand dollars? (Round your answer to at least one decimal place.)

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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