High School

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:

Answer :

Final answer:

The linear regression analysis suggests that there is a linear trend over time in the wavelength of light called "green". The regression equation for predicting wavelength from year is y = -0.1186t + 3.6032, where y is the wavelength less 500 and t is the years after 1900. The correlation coefficient for this data is r = -0.785, indicating a strong negative correlation. Using this information, the predicted wavelength for green in the year 1880 is approximately 3.485 millimeters.

Explanation:

To evaluate the linear trend over time in the wavelength of light called "green", we need to perform a linear regression analysis using the given data. The analysis involves finding the least-squares estimate of the straight-line regression function for predicting wavelength from the year.

First, we need to transform the data by subtracting 500 from the wavelength values and calculating the years after 1900 for each study. This will allow us to use the variables y and t in the regression analysis.

Next, we can calculate the regression equation by fitting a straight line to the data. The regression equation is of the form y = mx + b, where m is the slope and b is the intercept. The slope represents the change in y for each unit change in x, and the intercept represents the value of y when x is 0.

Using the regression equation, we can also calculate the correlation coefficient, which measures the strength and direction of the linear relationship between the variables. The correlation coefficient ranges from -1 to 1, where -1 indicates a perfect negative correlation, 1 indicates a perfect positive correlation, and 0 indicates no correlation.

Finally, we can use the regression equation to predict the wavelength for green in the year 1880 by substituting the value of t into the equation.

Learn more about linear regression analysis here:

https://brainly.com/question/35083892

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