/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 2 Explain the meaning of independe... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 13: Problem 2

Explain the meaning of independent and dependent variables for a regression model.

Short Answer

Expert verified
In a regression model, the independent variable (also known as the predictor) is the one that influences or is presumed to cause variations in the dependent variable. The dependent variable (or response variable) is what we are interested in predicting or explaining. The regression model examines how changes in the independent variables correspond to changes in the dependent variable.

Step by step solution

01

Define Independent Variable

The independent variable, also known as the predictor or explanatory variable, is the variable that affects the dependent variable. It is the variable that we have control over or we assume it keeps varying naturally and affects the outcome. In a regression model, we are interested in determining how changes in the independent variables lead to changes in the dependent variable.
02

Define Dependent Variable

The dependent variable, sometimes referred to as the response or outcome variable, is the variable we are interested in predicting or explaining in a regression model. It depends on the independent variable and it's the main factor we're trying to understand or predict.
03

Describe Interaction in Regression Model

In a regression model, the dependent variable is modeled as being directly influenced by independent variables. The aim is to establish if there's a significant relationship between the two. The strength and type of relationship (linear, exponential etc.) is represented by the model parameters which are estimated from the data.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A population data set produced the following information. $$ N=460, \quad \Sigma x=3920, \quad \Sigma y=2650, \quad \Sigma x y=26,570, \quad \Sigma x^{2}=48,530 $$ Find the population regression line.

Refer to Exercise \(13.25\). The data on ages (in years) and prices (in hundreds of dollars) for eight cars of a specific model are reproduced from that exercise. $$ \begin{array}{l|rrrrrrrr} \hline \text { Age } & 8 & 3 & 6 & 9 & 2 & 5 & 6 & 3 \\ \hline \text { Price } & 45 & 210 & 100 & 33 & 267 & 134 & 109 & 235 \\ \hline \end{array} $$ a. Do you expect the ages and prices of cars to be positively or negatively related? Explain. b. Calculate the linear correlation coefficient. c. Test at the \(2.5 \%\) significance level whether \(\rho\) is negative.

A sample data set produced the following information. $$ \begin{aligned} &n=12, \quad \Sigma x=66, \quad \Sigma y=588, \quad \Sigma x y=2244, \\ &\Sigma x^{2}=396, \quad \text { and } \quad \Sigma y^{2}=58,734 \end{aligned} $$ a. Calculate the linear correlation coefficient \(r\). b. Using the \(1 \%\) significance level, can you conclude that \(\rho\) is negative?

A population data set produced the following information. $$ \begin{aligned} &N=460, \quad \Sigma x=3920, \quad \Sigma y=2650, \quad \Sigma x y=26,570 \\ &\Sigma x^{2}=48,530, \text { and } \Sigma y^{2}=39,347 \end{aligned} $$ Find the linear correlation coefficient \(\rho\).

Consider the data given in the following table. $$ \begin{array}{l|llllll} \hline x & 10 & 20 & 30 & 40 & 50 & 60 \\ \hline y & 12 & 15 & 19 & 21 & 25 & 30 \\ \hline \end{array} $$ a. Find the least squares regression line and the linear correlation coefficient \(r\). b. Suppose that each value of \(y\) given in the table is increased by 5 and the \(x\) values remain unchanged. Would you expect \(r\) to increase, decrease, or remain the same? How do you expect the least squares regression line to change? c. Increase each value of \(y\) given in the table by 5 and find the new least squares regression line and the correlation coefficient \(r\). Do these results agree with your expectation in part b?
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Applied Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.