Income (in 1960 dollars/person) for European countries and the percent of the labor force (in %) that works in agriculture in 1960 are in the table below ('OECD economic development,' 2013). X, percent of labor in agriculture (in %) Y, income (in 1960 dollars/person) 4 1105 44 238 15 1242 23 681 27 504 14 1644 25 839 11 1361 36 529 18 1049 11 810 79 177 6 1005 20 977 42 290 20 1013 15 1035 56 324 a) State the random variables. rv X = of rv Y = of b) Make a scatterplot of X versus Y in StatCrunch (optional). Why do we wish to sketch a scatterplot? c) Find the equation of the best-fitting line (the least squares regression equation). Round values to 2 decimal places. Include the restricted domain. equation: = + * X restricted domain: % <= X <= % d) Interpret the slope from part c in the context of this problem. (Pay attention to the units) Every time we increase by we can expect to by on average. e) Interpret the Y-intercept from part c in the context of this problem. Include units. When is , we expect to be Does it make sense to interpret the Y-intercept on this problem? Why or why not? f) Should you use the regression equation to predict the income of a randomly selected European country that has a percent of labor in agriculture of 49 %? Should you use the regression equation to predict the income of a randomly selected European country that has a percent of labor in agriculture of 120 %? Looking at your answers above, predict the income for the one above that it made sense to do so. Make sure you use the stored equation and not the rounded equation from part c. Round final answer to 2 decimal places. The predicted income for a randomly selected European country that has a percent of labor in agriculture of % is g) Compute the residual for the following ordered pair in the data: (20, 977). Make sure you use the stored equation and not the rounded equation from part c. Round final answer to 2 decimal places. The residual for the European country with a percent of labor in agriculture of 20 % is Interpret what this value means in the context of this problem. The actual income of a randomly selected European country with a percent of labor in agriculture of 20 % is what was predicted.
Income (in 1960 dollars/person) for European countries and the percent of the labor force (in %) that works in agriculture in 1960 are in the table below ('OECD economic development,' 2013).
| X, percent of labor in agriculture (in %) | Y, income (in 1960 dollars/person) |
|---|---|
| 4 | 1105 |
| 44 | 238 |
| 15 | 1242 |
| 23 | 681 |
| 27 | 504 |
| 14 | 1644 |
| 25 | 839 |
| 11 | 1361 |
| 36 | 529 |
| 18 | 1049 |
| 11 | 810 |
| 79 | 177 |
| 6 | 1005 |
| 20 | 977 |
| 42 | 290 |
| 20 | 1013 |
| 15 | 1035 |
| 56 | 324 |
a) State the random variables.
rv X = of
rv Y = of
b) Make a
c) Find the equation of the best-fitting line (the least squares regression equation).
Round values to 2 decimal places.
Include the restricted domain.
equation: = + * X
restricted domain: % <= X <= %
d) Interpret the slope from part c in the context of this problem. (Pay attention to the units)
- Every time we increase by we can expect to by on average.
e) Interpret the Y-intercept from part c in the context of this problem. Include units.
- When is , we expect to be
Does it make sense to interpret the Y-intercept on this problem?
Why or why not?
f) Should you use the regression equation to predict the income of a randomly selected European country that has a percent of labor in agriculture of 49 %?
Should you use the regression equation to predict the income of a randomly selected European country that has a percent of labor in agriculture of 120 %?
Looking at your answers above, predict the income for the one above that it made sense to do so.
Make sure you use the stored equation and not the rounded equation from part c.
Round final answer to 2 decimal places.
- The predicted income for a randomly selected European country that has a percent of labor in agriculture of % is
g) Compute the residual for the following ordered pair in the data: (20, 977).
Make sure you use the stored equation and not the rounded equation from part c.
Round final answer to 2 decimal places.
The residual for the European country with a percent of labor in agriculture of 20 % is
Interpret what this value means in the context of this problem.
- The actual income of a randomly selected European country with a percent of labor in agriculture of 20 % is what was predicted.
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