Chapter 4: Q. 15 (page 192)
One use of the linear correlation coefficient is as a descriptive measure of the strength of the-------- relationshảp between two variables.
Linear
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For a data set consisting of two data points:
a. identify the regression line.
b. What is the sum of squared errors for the regression line? Explain your answer.
A positive linear relationship between two variables means that one variable tends to increase linearly as the other------
Sample Covariance. For a set of n data points, the sample covariance, is given by
The sample covariance can be used as an alternative method for tinding the slope and y-intercept of a regression line. The formulas are
where denotes the sample standard deviation of the x-values.
a. Use Equation (4.1) to determine the sample covariance of the data points in Exercise 4,45.
b. Use Equation (4.2) and your answer from part (a) to find the regression equation. Compare your result to that found in Exercise 4.57.
Answer true or false to each statement, and explain your answers.
a. The graph of a linear equation slopes upward unless the slope is 0 .
b. The value of the y-intercept has no effect on the direction that the graph of a linear equation slopes.
As we noted, because of the regression identity, we can express the coefficient of determination in terms of the total sum of squares and the error sum of squares as
a. Explain why this formula shows that the coefficient of determination can also be interpreted as the percentage reduction obtained in the total squared error by using the regression equation instead of the mean. . to predict the observed values of the response variable.
b.
What percentage reduction is obtained in the total squared error by using the regression equation instead of the mean of the observed prices to predict the observed prices?
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