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Chapter 13: Problem 5

Explain the difference between a simple and a multiple regression model.

Short Answer

Expert verified
Simple regression uses one independent variable to predict the value of a dependent variable, whereas multiple regression uses two or more independent variables for predictive analysis. Both are crucial tools in predictive analysis, with simple regression being advantageous for its simplicity whereas multiple regression proving more efficient for complex, multi-faceted data sets.

Step by step solution

01

Understanding Simple Regression

Simple regression is a predictive analysis tool that studies the relationship between two variables. A simple regression model helps to understand how the value of the dependent variable changes when there is a change in the value of the independent variable. For instance, a simple regression could be used to predict the sales of a bakery based on the number of hours it remains open.
02

Understanding Multiple Regression

Multiple regression is also a predictive analysis tool, but it extends to studying the relationship between more than two variables. In a multiple regression model, there is one dependent variable and multiple independent variables. It allows to evaluate the relative influence of these variables on the dependent variable. For example, multiple regression could be used to predict the sales of a bakery based not just on the number of hours it remains open, but also based on the number of employees working, cost of items, etc.
03

Contrasting Simple and Multiple Regression

The key difference between these two types of regression models lies in the number of independent variables. Where simple regression uses a single independent variable to predict the value of a dependent variable, multiple regression uses two or more independent variables for its predictions. Thus, while simple regression can provide fairly accurate predictions when there's only one influential factor, multiple regression tends to be more effective in real-world scenarios where outcomes are usually dependent on several factors.

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Most popular questions from this chapter

Explain the difference between exact and nonexact relationships between two variables. Give one example of each.

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The following information is obtained for a sample of 80 observations taken from a population. $$ \mathrm{SS}_{x x}=380.592, \quad s_{e}=.961, \text { and } \hat{y}=160.24-2.70 x $$ a. Make a \(97 \%\) confidence interval for \(B\). b. Test at the \(1 \%\) significance level whether \(B\) is negative. c. Can you conclude that \(B\) is different from zero? Use \(\alpha=.01\). d. Using a significance level of \(.025\), test whether \(B\) is less than \(-1.25\).

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The following table provides information on the speed at takeoff (in meters per second) and distance traveled (in meters) by a random sample of 10 world- class long jumpers. $$ \begin{array}{l|rrrrrrrrrr} \hline \text { Speed } & 8.5 & 8.8 & 9.3 & 8.9 & 8.2 & 8.6 & 8.7 & 9.0 & 8.7 & 9.1 \\ \hline \text { Distance } & 7.72 & 7.91 & 8.33 & 7.93 & 7.39 & 7.65 & 7.95 & 8.28 & 7.86 & 8.14 \\ \hline \end{array} $$ With distance traveled as the dependent variable and speed at takeoff as the independent variable, find the following: a. \(\mathrm{SS}_{x x}, \mathrm{SS}_{y y}\), and \(\mathrm{SS}_{x y}\) b. Standard deviation of errors c. SST, SSE, and SSR d. Coefficient of determination
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