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Chapter 4: Q. 4.85 (page 181)

4.85 A measure of the amount of variation in the observed values of the response variable explained by the regression is the-----. The mathematical abbreviation for it is----.

Short Answer

Expert verified

A measure of the amount of variation in the observed values of the response variable explained by the regression is the Regression Sum of a square.

The mathematical abbreviation for it is SSR

Step by step solution

01

Given Information

To determine the blank in the given statement.

02

Explanation

The regression sum of the square is a metric for calculating the amount of squared variance in the observed values of the response variable explained by the regression. The regression sum of squares formula is as follows:

SSR=鈭�yi^-y炉2

As a result, the regression sum of the square is a measure of the amount of variance in the observed values of the response variable explained by the regression. SSR is the mathematical abbreviation for it.

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Most popular questions from this chapter

Corvette Prices. In Exercise 4.59. you determined a regression equation that can be used to predict the price of a Corvette, given its age.

a. Should that regression equation be used to predict the price of a 4-year-old Corvette? a 10-year-old Corvette? Explain your answers.

b. For which ages is the use of the regression equation to predict price reasonable?

Acreage and Value. The document Arizona Residential Property Valuation System, published by the Arizona Department of Revenue, describes how county assessors use computerized systems to value single-family residential properties for property tax purposes. On the Weiss Stats site are data on lot size (in acres) and assessed value (in thousands of dollars) for a sample of homes in a particular area.

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).

High and Low Temperature. The data from Exercise 4.75 for average high and low temperatures in January for a random sample of 50cities are on the WeissStats site.

a. decide whether use of the linear correlation coefficient as a descriptive measure for the data is appropriate. If so, then also do parts (b) and (c).

b. obtain the linear correlation coefficient.

c. interpret the value of rin terms of the linear relationship between the variables in question.

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 .

Gas Gurzlers. The data for gas mileage and engine displacement for 121vehicles from Exercise 4.78 are provided on the WeissStats site.

a. decide whether the use of the linear correlation coefficient as a descriptive measure for the data is appropriate. If so, then also do parts (b) and (c).

b. obtain the linear correlation coefficient.

c. interpret the value of r in terms of the linear relationship between the mo variables in question.
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