File Name: correlation and regression examples .zip
Introduction to Fixed regression, or propensity scores. Sketch the regression line.
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. In some cases it might be impossible to tell from the information given. The slope is positive.
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. Inferential tests can be run on both the correlation and slope estimates calculated from a random sample from a population.
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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.
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.
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When investigating the relationship between two or more numeric variables, it is important to know the difference between correlation and regression.