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Unformatted text preview: 1 Simple Regression  Part 1 1 Simple Linear Regression Chapter 13 Simple Regression  Part 1 2 Correlation & Regression h We will investigate the relationship between two variables, Y and X h In general, we want to answer the question: “ Does X tell us something about how Y behaves?” 2 Simple Regression  Part 1 3 Textbook’s Example h At Sunflowers Apparel, how well can you predict sales by the size of the store? h You would naturally think that more stuff on display ==> higher sales. h Sales from 14 stores are in Site.xls . Simple Regression  Part 1 4 Exploring the data h We use an XY scatter plot to display both the strength and type of relationship. h We use the correlation coefficient to summarize the strength of the relationship. 3 Simple Regression  Part 1 5 Scatter Plot of Sales versus Store Size 2 4 6 8 10 12 14 1 2 3 4 5 6 7 Square Feet (1000s) Annual Sales (Millions) The example Correlation = ? Simple Regression  Part 1 6 Computing r h Many of you can do this with the calculators you used in STA 2023 h Our text covers this back in the descriptive statistics chapter 3. h Page 116: y x S S Y X Cov r ) , ( = 4 Simple Regression  Part 1 7 Computations Store Square Feet Annual Sales 1 1.7 3.7 4.523367 Covar 2 1.6 3.9 2.999414 SD sales 3 2.8 6.7 1.707981 SD SqFt 4 5.6 9.5 5 1.3 3.4 0.950883 Correl 6 2.2 5.6 7 1.3 3.7 8 1.1 2.7 9 3.2 5.5 10 1.5 2.9 11 5.2 10.7 12 4.6 7.6 13 5.8 11.8 14 3 4.1 Simple Regression  Part 1 8 Excel and PhStat notes h PhStat has the Scatter Plot off the descriptive statistics menu. h Excel has functions COVAR and CORREL. h Correlation not directly in PhStat, but there are templates Covariance.xls and Correlation.xls. 5 Simple Regression  Part 1 9 What is covariance? h It measures how much X and Y tend to vary in the same direction. h Positive covariance means ___________. A negative covariance means _________. h However, it is hard to interpret because there is no “standard”. What does the covariance of 4.52 mean? If store size was in actual square footage, covariance would be 4524....
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This note was uploaded on 02/14/2011 for the course QMB 3250 taught by Professor Thompson during the Spring '08 term at University of Florida.
 Spring '08
 Thompson

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