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:
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