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Linear Regression and Correlation

Chapter 13


©The McGraw-Hill Companies, Inc. 2008

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Understand and interpret the terms dependent and independent variable. Calculate and interpret the coefficient of correlation, the coefficient of determination, and the standard error of estimate. Conduct a test of hypothesis to determine whether the coefficient of correlation in the population is zero. Calculate the least squares regression line. Construct and interpret confidence and prediction intervals for the dependent variable.


Regression Analysis - Introduction

Recall in Chapter 4 the idea of showing the relationship between two variables with a scatter diagram was
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The Independent Variable provides the basis for estimation. It is the predictor variable.


Regression Example
The sales manager of Copier Sales of America, which has a large sales force throughout the United States and Canada, wants to determine whether there is a relationship between the number of sales calls made in a month and the number of copiers sold that month. The manager selects a random sample of 10 representatives and determines the number of sales calls each representative made last month and the number of copiers sold.


Scatter Diagram


The Coefficient of Correlation, r
The Coefficient of Correlation (r) is a measure of the strength of the relationship between two variables. It requires interval or ratio-scaled data.  It can range from -1.00 to 1.00.  Values of -1.00 or 1.00 indicate perfect and strong correlation.  Values close to 0.0 indicate weak correlation.  Negative values indicate an inverse relationship and positive values indicate a direct relationship.


Perfect Correlation


Minitab Scatter Plots


Correlation Coefficient - Interpretation


Correlation Coefficient - Formula


Coefficient of Determination
The coefficient of determination (r2) is the proportion of the total variation in the dependent variable (Y) that is explained or accounted for by the variation in the independent variable (X). It is the

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