Chapter17_STAT1100_LC.ppt", filename="Chapter17_STAT1100_LC.ppt", filename="Chap

Chapter17_STAT1100_LC.ppt", filename="Chapter17_STAT1100_LC.ppt", filename="Chap

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Simple Linear Regression and Correlation Statistics for Management and Economics Chapter 17

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FIRST! A REVIEW!! Graphing the relationship between two interval variables (chapter 2) Measures of Linear Relationship (ch.4) Covariance Correlation
Graphical Comparison Between Two Interval Variables Sometimes we are interested in how two interval variables are related. To explore this relationship, we employ a scatter diagram or scatterplot , which plots two variables against one another. The independent (predictor, explanatory) variable is labeled X and is usually placed on the horizontal axis, while the other, dependent (outcome, response) variable, Y, is mapped to the vertical axis.

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Scatterplot Collect the data – size and selling price of homes. Determine the independent variable (X – house size) and the dependent variable (Y – selling price) Use Excel to create a “scatter diagram”…
Interpretation: Scatterplot Positive Linear Relationship Negative Linear Relationship Weak or Non-Linear Relationship Strength The extent to which the data points fit the pattern in the plot Pattern Do the data fall in a linear pattern? The pattern tells us if there is a relationship or not Direction The direction in which the data fall – tells important information about the relationship

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Scatterplot: Furnace Energy BTU.In BTU.Out 20 15 10 5 5 Scatterplot of BTU.Out vs BTU.In Direction? Strength? Pattern?
Measures of Linear Relationship Numerical measures of linear relationship that provide information as to the strength & direction of a linear relationship (if any) between two variables. Covariance - is there any pattern to the way two variables move together? Coefficient of correlation - how strong is the linear relationship between two variables?

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Interpretation: Covariance When two variables move in the same direction (both increase or both decrease), the covariance will be a large positive number . When two variables move in opposite directions , the covariance is a large negative number . When there is no particular pattern , the covariance is a small number .
Example: Covariance A commodities trader contacted a Midwest supplier of field corn seed to learn about demand. The supplier provided the average price per bushel (in dollars) and the number of bushels sold (in thousands) for an eight-year period. Price Sales Price 0.195 Sales -9.96875 556.25 Price Sales XiYi 1.25 125 156.25 1.75 105 183.75 2.25 65 146.25 2 85 170 2.5 75 187.5 2.25 80 180 2.7 50 135 2.5 55 137.5 17.2 640 1296.25 s xy = (1/(8-1)) [ 1296.25 - (17.2 * 640)/8)] = 0.143 * -79.75 = -11.40 What does this tell us about the relationship?

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Measures of Linear Relationship: Correlation Greek letter “rho” The Coefficient of Correlation (a.k.a., the correlation) is the covariance divided by the standard deviations of the variables From the correlation, we can determine the strength, direction, and linearity of the association between X and Y. The correlation is the “numerical scatterplot”
Interpretation: The Correlation and the Scatterplot ρ or r = +1 0 -1 Strong positive linear relationship No linear relationship Strong negative linear relationship

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This note was uploaded on 06/25/2008 for the course BUSSPP MCE taught by Professor Atkins during the Spring '08 term at Pittsburgh.

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Chapter17_STAT1100_LC.ppt", filename="Chapter17_STAT1100_LC.ppt", filename="Chap

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