Notes - Chapter 13 - MGMT 2340 Section W01 Business...

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MGMT 2340 Section W01 Business Statistics I Instructor: E. Mark Leany contact via Blackboard online.uen.org alternately: [email protected] Chapter 13 Linear Regression and Correlation 444
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GOALS 1. Understand and interpret the terms dependent and independent variable . 2. Calculate and interpret the coefficient of correlation , the coefficient of determination , and the standard error of estimate . 3. Conduct a test of hypothesis to determine whether the coefficient of correlation in the population is zero. 4. Calculate the least squares regression line. 5. Construct and interpret confidence and prediction intervals for the dependent variable. 444 Regression Analysis - Introduction z Chapter 4 - idea of showing the relationship between two variables with a scatter diagram was introduced. z Example: As the age of the buyer increased, the amount spent for the vehicle also increased. z Correlation: Numerical measures to express the strength of relationship between two variables are developed. z Regression: An equation is used to express the relationship between variables, allowing us to estimate one variable on the basis of another. 456
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Regression Analysis - Examples 1. Is there a relationship between the amount Healthtex spends per month on advertising and its sales in the month? 2. Can we base an estimate of the cost to heat a home in January on the number of square feet in the home? 3. Is there a relationship between the miles per gallon achieved by large pickup trucks and the size of the engine? 4. Is there a relationship between the number of hours that students studied for an exam and the score earned? 456 The Independent Variable provides the basis for estimation. It is the predictor variable - scaled on the X axis Correlation Analysis Correlation Analysis is the study of the relationship between variables. It is also defined as group of techniques to measure the association between two variables . Scatter Diagram is a chart that portrays the relationship between the two variables. It is the usual first step in correlations analysis The Dependent Variable is the variable being predicted or estimated - scaled on the Y axis 456
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Scatter Diagram 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. 456 The Coefficient of Correlation, r z r is used to estimate ȡ (rho) z It shows the direction and strength of the linear relationship between two interval or ratio-scale variables z It can range from -1.00 to +1.00.
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