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The accompanying plot and regression output show the federal rate on 3-month Treasury bills from 1950 to 1980 and a regression model fit to the relationship between the Rate (in %) and Years.

a) What is the correlation between Rate and Year? (Round to two decimal places as needed.)
b) What is the intercept of the regression model?

User Ed Knowles
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1 Answer

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Final answer:

The correlation coefficient and intercept in a regression analysis can be found in the regression output or calculated using all pairs of data for 'Rate' and 'Year'. The y-intercept represents the federal rate on 3-month Treasury bills at year 0, and the significance of the correlation depends on its value and the associated p-value.

Step-by-step explanation:

To address the student's question regarding the correlation between the federal rate on 3-month Treasury bills and the year, as well as the intercept of the regression model, specific data values and regression output would be required. However, given that we don't have the actual plot or regression output, let's go through the steps on how to find the answers once those are provided.

Determining Correlation and Intercept

  1. Correlation Coefficient: To find the correlation between Rate and Year, one would look for the coefficient (r) in the regression output. If the output is not provided, you can calculate the correlation coefficient using a statistical software or calculator by inputting all the pairs of 'Rate' and 'Year'.
  2. Regression Intercept: The intercept (often represented as 'a' in a regression equation of the form ŷ = a + bx) is the value where the fitted line crosses the Y-axis. In the regression output, this would typically be labeled as the 'Intercept' or 'Constant'.

If the student provides the regression output or the scatter plot, the exact values for the correlation coefficient and the intercept can be determined and interpreted accordingly.

Relevance of the Y-Intercept

In the context of the question, the y-intercept would represent the hypothetical federal rate on 3-month Treasury bills at year 0 (which is not meaningful in this context as the data starts from 1950).

Significance of the Correlation Coefficient

Whether a correlation is significant depends on its value and possibly the p-value associated with it. A value close to 1 or -1 indicates a strong relationship, whereas a value close to 0 suggests little to no linear relationship. The p-value helps us determine if the observed correlation is statistically significant.

User Arnel
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