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**Correlation and Regression Analysis**

Statistics Correlation and Regression Analysis Alan D. Smith

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Correlation and Regression Analysis

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**GOALS TO DRAW SCATTER DIAGRAMS.**

TO CALCULATE AND DISCUSS PEARSON’S CORRELATION COEFFICIENT. TO CALCULATE AND DISCUSS THE COEFFICIENT OF DETERMINATION. TO USE THE LEAST SQUARES METHOD TO DETERMINE THE REGRESSION EQUATION. USING EXCEL FOR REGRESSION ANALYSIS

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CORRELATION ANALYSIS Correlation Analysis - A group of statistical techniques used to measure the strength of the relationship (correlation) between two variables. Scatter Diagram - a chart that portrays the relationship between the two variables of interest. Dependent Variable - the variable that is being predicted or estimated. Independent Variable - the variable that provides the basis for estimation. It is the predictor variable.

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**THE COEFFICIENT OF CORRELATION, r**

The Coefficient of Correlation, r - is a measure of the strength of the linear relationship between two variables. It can range from to Values of or 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.

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**PERFECT NEGATIVE CORRELATION**

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**PERFECT POSITIVE CORRELATION**

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ZERO CORRELATION

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**STRONG POSITIVE CORRELATION**

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FORMULA FOR r

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**COEFFICIENT OF DETERMINATION, r2**

The Coefficient of Determination, r2 - 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. The coefficient of determination is the square of the coefficient of correlation. It can range from 0 to 1.0.

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EXAMPLE Lance Engle is president of the student body at The Computer University (CU). He is concerned about the cost of textbooks at CU. To provide insight into the problem he selects a sample of eight textbooks currently on sale in the bookstore. He decides to study the relationship between the number of pages in the text and cost. The collected data is given on the next slide. Compute the correlation coefficient. Answer: r = 0.614

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EXAMPLE (continued)

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EXAMPLE (continued)

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REGRESSION ANALYSIS Purpose - to determine the regression equation. It is used to predict the value of one variable (Y, called the dependent variable) based on another variable (X, called the independent variable). Procedure: Select a sample from the population, and list the paired data (X, Y) for each observation. Draw a scatter diagram to give a visual portrayal of the relationship. Determine the regression equation Y = a + bX.

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REGRESSION ANALYSIS Y is the average predicted value of Y for any X. a is the Y-intercept, or the estimated Y value when X = 0. b is called the slope of the line. It is the average change in Y for each change of one unit in X. The least squares principle is used to obtain a and b and are given by:

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EXAMPLE (continued) Develop a regression equation for the information given in the EXAMPLE that can be used to estimate the selling price based on the number of pages. b = , a = Y = X . What is the estimated selling price of a 650-page book? Y = (650) = $27.14.

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Chapter 12 Homework Chapter 12: CD-ROM

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EXCEL Tools Data Analysis Regression

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FOR NEXT TIME Please read Chapter 13 : ANOVA

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