(a)
To explain: the observed variation in yearly changes in the index
(a)
Answer to Problem 50E
About 35.52% of the variation in Y is due to the straight line relationship between Y and X.
The other 64.48% is individual variation that is not explained by the linear relationship.
Explanation of Solution
Given:
Mean | Standard deviation | |
Percent change in a stock market index in January | ||
Percent change in a stock market index for the entire year |
Calculation:
The least-squares regression line of percent change in a stock market index for the entire year on percent change in a stock market index for the January has slope is
To find the intercept, we use the fact that the least-squares line passes through
So the equation of the least-squares line is:
The coefficient of determination
Here,
Then about 35.52% of the variation in Y is due to the straight line relationship between Y and X. The other 64.48% is individual variation that is not explained by the linear relationship.
Conclusion:
Hence, about 35.52% of the variation in Y is due to the straight line relationship between Y and X. The other 64.48% is individual variation that is not explained by the linear relationship.
(b)
To explain:the value of thestandard deviation
(b)
Answer to Problem 50E
The standard deviationof the residuals
Explanation of Solution
Explanation:
For these data the standard deviation of the residuals is
The standard deviation of the residuals
Chapter 3 Solutions
The Practice of Statistics for AP - 4th Edition
Additional Math Textbook Solutions
An Introduction to Mathematical Statistics and Its Applications (6th Edition)
Statistics: The Art and Science of Learning from Data (4th Edition)
Statistics for Psychology
Elementary Statistics: Picturing the World (7th Edition)
Fundamentals of Statistics (5th Edition)
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