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Chapter 4: Q. 4.38 (page 173)

Using the regression equation to make predictions for the values of the predictor variable outside the range of the observed values of the predictor variable is called _____.

Short Answer

Expert verified

Extrapolation is a method for predicting values of the predictor variable that are outside of the range of the predictor variable's observed values.

Step by step solution

01

Given information 

We need to find out what the method is for making predictions for values of the predictor variable that are beyond the range of the observed values of the predictor variable.

02

Explanation 

The link between the x variable (or predictor variable) and the y variable (or response variable) is predicted by regression equation. Extrapolation is the process of making predictions outside the range of this data. The association between variables does not hold true outside of the range.

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Most popular questions from this chapter

Tine Series. A collection of observations of a variable y taken at regular intervals over time is called a time series. Bocoomsic data and electrical signals are examples of time series. We can think of a time series as providing data points x1+y2where x0is the ith observation time and yiis the observed value of y at time xi. If a time series exhibits a linear trend, we can find that trend by determining the regression equation for the data points. We can then use the regression equation for forecasting purposes.

As an illustration, consider the data on the WeissStats site that shows the U.S. population, in millions of persons, for the years 1900 2013. as provided by the I.S. Census Beret.

a. Use the technology of your choice to lesbian a scatterplot of the data.

h. Use the technology of your choice to find the regression equation.

6. Use your result from part (b) to forecast the U.S. population for the years 2014 and 2015 .

10. The line that best fits a set of data points according to the least-squares criterion is called the________line.

Sample Covariance. For a set of n data points, the sample covariance, sxy+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

b1=sv/xk2andb0=y^-b1i^n

where sidenotes 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.

For which of the following sets of data points can you reasonably determine a regression line? Explain your answer.

Age and Price of Orions. In Table 4.2, we provided data on age and price for a sample of 11Orions between 2and 7years old. On the Weiss Stats site, we have given the ages and prices for a sample of 31Orions between 1and 11years old.

a. Obtain a scatterplot for the data.

b. Is it reasonable to find a regression line for the data? Explain your answer.
See all solutions

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