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Chapter 4: Q. 3 (page 191)
Theintercept of a line has no effect on the steepness of the line.
The intercept of a line has no effect on the steepness of the line". The given statement is true.
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4.78 Gas Guzzlers. The magazine Consumer Reports publishes information on automobile gas mileage and variables that affect gas mileage. In one issue, data on gas mileage (in miles per gallon) and engine displacement (in liters) were published for vehicles. Those data are available on the Weiss Stats site.
a. Obtain a scatterplot for the data.
b. Decide whether finding a regression line for the data is reasonable. If so, then also do parts (c) (f).
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.
In Exercise 4.11, we give linear equations. For each equation,
a. find the -intercept and slope.
b. determine whether the line slopes upward, slopes downward, or is horizontal, without graphing the equation.
c. use two points to graph the equation.
Given equation is,
9. Based on the least-squares criterion, the line that best fits a set of data points is the one with the ________possible sum of squared errors.
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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