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 18 1049 23 681 42 290 6 1005 36 529 15 1035 20 1013 20 977 11 1361 56 324 25 839 14 1644 79 177 15 1242 27 504 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 <= %
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 |
| 18 | 1049 |
| 23 | 681 |
| 42 | 290 |
| 6 | 1005 |
| 36 | 529 |
| 15 | 1035 |
| 20 | 1013 |
| 20 | 977 |
| 11 | 1361 |
| 56 | 324 |
| 25 | 839 |
| 14 | 1644 |
| 79 | 177 |
| 15 | 1242 |
| 27 | 504 |
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 36 %?
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 128 %?
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: (27, 504).
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 27 % 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 27 % is what was predicted.
Trending now
This is a popular solution!
Step by step
Solved in 5 steps with 2 images
