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------------------------------------------------ This data is modeled on Stevens (1966), citing Dimmick and Hubbard (1939), which reported data from 20 studies of the color perception of unitary hues. The wavelength (in nanometers) of light called "green" by subjects in each experiment is given in the following table, along with the year the study was conducted.

| Study | Wavelength | Date |
|-------|------------|------|
| 1 | 536 | 1886 |
| 2 | 497 | 1888 |
| 3 | 528 | 1934 |
| 4 | 507 | 1910 |
| 5 | 514 | 1925 |
| 6 | 520 | 1915 |
| 7 | 500 | 1923 |
| 8 | 511 | 1935 |
| 9 | 508 | 1912 |
| 10 | 531 | 1874 |
| 11 | 528 | 1888 |
| 12 | 501 | 1911 |
| 13 | 504 | 1921 |
| 14 | 505 | 1897 |
| 15 | 504 | 1933 |
| 16 | 506 | 1899 |
| 17 | 516 | 1939 |
| 18 | 499 | 1928 |
| 19 | 514 | 1918 |
| 20 | 530 | 1932 |

These data suggest the question: Is there any linear trend over time in the wavelength of light called "green"? Evaluate this question by finding the least-squares estimate of the straight-line regression function for predicting wavelength from year. For this analysis, [tex]y[/tex] is the wavelength less 500, and [tex]t[/tex] is the years after 1900. (Hint: This will require some minor data transformation.)

1. Give the regression equation (using the variables [tex]y[/tex] and [tex]t[/tex], reporting slope and intercept accurate to at least three decimal places).

2. Find the correlation coefficient for this data: [tex]r =[/tex]

3. Using this information, predict the wavelength for green in the year 1880: wavelength =

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For used cars of a given make and model less than 10 years old that were sold in the past 6-18 months, the relationship between the sale price (in $1000s) and the mileage (in 1000 miles) was estimated using simple bivariate regression. Here is the summary of the output from the statistical software package used:

- (Intercept): 26.7543
- Mileage:
- Residual Standard Error:
- R-squared: 0.7159

In this format, the intercept does not have an authentic interpretation. In other words, the intercept is the cost of a used car with 0 miles, which would be called a new car, not a used car. So, you decide to transform the predictor variable and then rerun the model. In particular, you decide to re-center the mileage variable at 10 thousand miles. In other words, you subtract 10 from all of the mileage values (recall, mileage is reported in this data in 1000 miles). While you could actually transform the data and then rerun the model in your statistical software package, this is not necessary.

Give the 4 parameters that you would obtain in the output for the model with the re-centered predictor variable:

- (Intercept):
- Mileage:
- Residual Standard Error:
- R-squared: