Question

The data for personal income per capita, in thousands of dollars, and per capita beer consumption, in gallons, for 20 states is given in the table. Use the technology of your choice to complete parts (a) through (d). Click the icon to view the data. a. Decide whether finding a regression line for the data is reasonable. If so, then also do parts (b) through (d). For the purposes of this regression, let Income be the explanatory variable (x) and let Beer be the response variable (y). There is \to the data, so it is \to carry out a linear regression. b. Compute the coefficient of determination, $r^2$. Select the correct choice below and, if necessary, fill in the answer box within your choice. OA. $r^2 = $ (Round to three decimal places as needed.) B. It is not appropriate to carry out a linear regression. c. Determine the percentage of variation in the observed values of the response variable explained by the regression, and interpret your answer. Select the correct choice below and, if necessary, fill in the answer box within your choice. A. About % of the variation in beer consumption is explained by personal income. (Round to one decimal place as needed.) B. About % of the variation in personal income is explained by beer consumption. (Round to one decimal place as needed.) C. It is not appropriate to carry out a linear regression. d. State how useful the regression equation appears to be for making predictions. A. Moderately useful B. Very useful C. Not useful D. It is not reasonable to carry out a linear regression. Income and Beer Consumption Income Beer 45 25.5 45.1 30 41.9 33.6 36.9 25.7 44.8 29.1 36.9 25.9 42.1 33.6 35 24.4 39.5 34 52 23.2 46.2 28.5 33.1 33.9 37.4 35.8 47.1 43.9 52.1 22.4 51.9 45.8 39.3 30.1 43 35.3 47.1 26.7 34.5 30.3

          The data for personal income per capita, in thousands of dollars, and per capita beer consumption, in gallons, for 20 states is given in the table. Use the technology of your choice to complete parts (a) through (d).
Click the icon to view the data.
a. Decide whether finding a regression line for the data is reasonable. If so, then also do parts (b) through (d).
For the purposes of this regression, let Income be the explanatory variable (x) and let Beer be the response variable (y).
There is \to the data, so it is \to carry out a linear regression.
b. Compute the coefficient of determination, $r^2$. Select the correct choice below and, if necessary, fill in the answer box within your choice.
OA. $r^2 = $ (Round to three decimal places as needed.)
B. It is not appropriate to carry out a linear regression.
c. Determine the percentage of variation in the observed values of the response variable explained by the regression, and interpret your answer. Select the correct choice below and, if necessary, fill in the answer box within your choice.
A. About % of the variation in beer consumption is explained by personal income.
(Round to one decimal place as needed.)
B. About % of the variation in personal income is explained by beer consumption.
(Round to one decimal place as needed.)
C. It is not appropriate to carry out a linear regression.
d. State how useful the regression equation appears to be for making predictions.
A. Moderately useful
B. Very useful
C. Not useful
D. It is not reasonable to carry out a linear regression.
Income and Beer Consumption
Income	Beer
45	25.5
45.1	30
41.9	33.6
36.9	25.7
44.8	29.1
36.9	25.9
42.1	33.6
35	24.4
39.5	34
52	23.2
46.2	28.5
33.1	33.9
37.4	35.8
47.1	43.9
52.1	22.4
51.9	45.8
39.3	30.1
43	35.3
47.1	26.7
34.5	30.3

The data for personal income per capita, in thousands of dollars, and per capita beer consumption, in gallons, for 20 states is given in the table. Use the technology of your choice to complete parts (a) through (d).
Click the icon to view the data.
a. Decide whether finding a regression line for the data is reasonable. If so, then also do parts (b) through (d).
For the purposes of this regression, let Income be the explanatory variable (x) and let Beer be the response variable (y).
There is →the data, so it is →carry out a linear regression.
b. Compute the coefficient of determination, r^2. Select the correct choice below and, if necessary, fill in the answer box within your choice.
OA. r^2 = (Round to three decimal places as needed.)
B. It is not appropriate to carry out a linear regression.
c. Determine the percentage of variation in the observed values of the response variable explained by the regression, and interpret your answer. Select the correct choice below and, if necessary, fill in the answer box within your choice.
A. About % of the variation in beer consumption is explained by personal income.
(Round to one decimal place as needed.)
B. About % of the variation in personal income is explained by beer consumption.
(Round to one decimal place as needed.)
C. It is not appropriate to carry out a linear regression.
d. State how useful the regression equation appears to be for making predictions.
A. Moderately useful
B. Very useful
C. Not useful
D. It is not reasonable to carry out a linear regression.
Income and Beer Consumption
Income Beer
45 25.5
45.1 30
41.9 33.6
36.9 25.7
44.8 29.1
36.9 25.9
42.1 33.6
35 24.4
39.5 34
52 23.2
46.2 28.5
33.1 33.9
37.4 35.8
47.1 43.9
52.1 22.4
51.9 45.8
39.3 30.1
43 35.3
47.1 26.7
34.5 30.3

Added by Brandon P.

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