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Correlation And Regression In Statistics Pdf

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10.E: Correlation and Regression (Exercises)

When the goal of a researcher is to evaluate the relationship between variables, both correlation and regression analyses are commonly used in medical science. Although related, correlation and regression are not synonyms, and each statistical approach is used for a specific purpose and is based on a set of specific assumptions. Regression is indicated when one of the variables is an outcome and the other one is a potential predictor of that outcome, in a cause-and-effect relationship. If the outcome is a continuous variable, a linear regression model is indicated, and, if it is binary, a logistic regression is used. Regression also quantifies the direction and strength of the relationship between two numeric variables, X the predictor and Y the outcome ; however, in contrast with correlation, these two variables are not interchangeable, and correctly identifying the outcome and the predictor is key. Regression models additionally permit the evaluation of more than one predictor variable, another important difference from correlation analysis. Important assumptions of linear regression are normality and linearity of the outcome variable, independence between the two variables, and equal variance of the outcome variable across the regression line.

In many studies, we measure more than one variable for each individual. For example, we measure precipitation and plant growth, or number of young with nesting habitat, or soil erosion and volume of water. We collect pairs of data and instead of examining each variable separately univariate data , we want to find ways to describe bivariate data , in which two variables are measured on each subject in our sample. Given such data, we begin by determining if there is a relationship between these two variables. As the values of one variable change, do we see corresponding changes in the other variable? We can describe the relationship between these two variables graphically and numerically.

A correlation or simple linear regression analysis can determine if two numeric variables are significantly linearly related. A correlation analysis provides information on the strength and direction of the linear relationship between two variables, while a simple linear regression analysis estimates parameters in a linear equation that can be used to predict values of one variable based on the other. The Pearson correlation coefficient, r , can take on values between -1 and 1. A general form of this equation is shown below:. The slope, b 1 , is the average change in Y for every one unit increase in X. Beyond giving you the strength and direction of the linear relationship between X and Y , the slope estimate allows an interpretation for how Y changes when X increases.

10.E: Correlation and Regression (Exercises)

These are homework exercises to accompany the Textmap created for "Introductory Statistics" by Shafer and Zhang. With the exception of the exercises at the end of Section Save your computations done on these exercises so that you do not need to repeat them later. For the Basic and Application exercises in this section use the computations that were done for the exercises with the same number in Section For the Basic and Application exercises in this section use the computations that were done for the exercises with the same number in previous sections.

10.E: Correlation and Regression (Exercises)

The present review introduces methods of analyzing the relationship between two quantitative variables. The calculation and interpretation of the sample product moment correlation coefficient and the linear regression equation are discussed and illustrated. Common misuses of the techniques are considered. Tests and confidence intervals for the population parameters are described, and failures of the underlying assumptions are highlighted. The most commonly used techniques for investigating the relationship between two quantitative variables are correlation and linear regression.

Statistics review 7: Correlation and regression

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Simple Linear Regression

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Chapter 7: Correlation and Simple Linear Regression


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The use of correlation and regression as applied to the analysis of family resemblance is discussed.