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Chapter 4: Q. 8 (page 192)

8. Regarding the variables in a regression analysis.

a. what is the independent variable called?

b. what is the dependent variable called?

Short Answer

Expert verified

a. The predictor variable or explanatory variable is the independent variable.

b. The response variable, often known as the explained variable, is the dependent variable.

Step by step solution

01

Part (a) Step 1: Concept Introduction

Statistical regression analysis enables you to determine the relationship between two or more variables. Whenever, to predict a continuous dependent variable, then regression analysis has been used.

02

Part (a) Step 2: Explanation 

Take, for example, regression analysis.

To predict the values, regression is utilized.

The risk factors are referred to as predictors in the regression process.

As a result, the independent variable is referred to as the predictor or explanatory variable.

03

Part (b) Step 1: Concept Introduction

Statistical regression analysis enables you to determine the relationship between two or more variables. Whenever, to predict a continuous dependent variable, then regression analysis has been used.

04

Part (b) Step 2: Explanation 

Take, for example, regression analysis.

To predict the values, regression is utilized.

As a result, the dependent variable is referred to as a response or explained variable.

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Most popular questions from this chapter

One use of the linear correlation coefficient is as a descriptive measure of the strength of the-------- relationshảp between two variables.

For each exercise, determine the linear correlation coefficient by using

a. Definition 1.8 on page 183.

b. Formada 4.4 a pace 185.

Compare your answers in parts a) and (b).

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 r2=1-SSE/SST

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. Y¯. to predict the observed values of the response variable.

b.

x
6
6
6
2
2
5
4
5
1
4
y
290
280
295
425
384
315
355
325
425
325

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?

Shortleaf Mines. The ability to estimate the volume of a tree based on a simple measurement, such as the tree's diameter, is important to the lumber industry, ecologists, and conservationists. Data on volume, in cubic feet. and diameter at breast height, in inches, for 70shortlist pics were reported in C. Bruce and F. X. Schumacher's hopes Mensuration (New York: McGraw-Hill. 1935) and analyzed by A. C. Atkinson in the article "Transforming Both Sides of a Tree" (The Anarricas Slasisiciun, Vol, 48, PD. 307-312), The data are presented on the WeissStats site.

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Tax Efficiency. In Exercise 4.58, you determined a regression equation that relates the variables percentage of investments in energy securities and tax efficiency for mutual fund portfolios.

a. Should that regression equation be used to predict the tax efficiency of a mutual fund portfolio with 6.4%of its investments in energy securities? with 15%of its investments in energy securities? Explain your answers.

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