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For the data below, the correlation coefficient between the two variables is r = 0
For the data below, the correlation coefficient between the two variables is r = 0.9733 and the least squares regression line is approximately ? = 0.1x + 59.
| Yearly Income (thousands) (x) | Grade (y) |
|---|---|
| 50 | 60 |
| 100 | 75 |
| 200 | 80 |
| 250 | 85 |
| 300 | 90 |
| 400 | 100 |
(a) Draw the scatter plot corresponding to the table.
(b) Find the coefficient of determination and comment on the quality of the model.
(c) What number gives the intercept of the regression line, and what dies it represent in this example?
(d) What grade would you expect someone to earn if their family's yearly income was $150,000?
(e) What grade would you expect someone to earn if their family's yearly income was a million dollars?
(f) Comment on the trustworthiness of these predictions.
(g) Based on this can you conclude that wealth and intelligence are causally related?
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