Class 3 - Linear Association

# Class 3 - Linear Association - Linear Association between T...

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Unformatted text preview: Linear Association between T wo Quantitative Var iab We will use three methods to assess linear association between two quantitative variables. 1. X-Y Scatter plot If one variable is clearly a variable who's value is a respo the value of another variable then the r esponse var iable (dependent variable) is on the Y or ver tical axis and the explanator y var iable (independent variable) is on the X or hor izontal axis . Examine the scatterplot to visually determine if there appears to be an associatio between the two variables. 2. The Cor r elation Coefficient (r ) is a unit-free measure of the amount linear association (relationship) between two quantitative variables. Measureme values range from -1 to +1. r=0 implies no linear association. The amount or st of linear association increases as r departs from 0 moving toward either -1 or +1. implies a positive assocation where one expects the value of one variable to incre the value of the other increases. r&lt;0 implies a negative assocation where one expec value of one variable to decrease if the value of the other increases. If r=-1 or if r=1, th are all exactly on a straight line having negative slope for r=-1 and a positive slope for r= Since other measures of correlation exist , the coefficient used in this class and by the te often called the Pearson Correlation Coefficient. 3. Linear Regr ession uses the data to estimate the values to determine a linea equation to describe the relationship between the two quantitative variables using the explanatory variable (independent or X variable) to predict the response variable (depen or Y variable). bles onse to plotted plotted on t of ent trength . r&gt;0 ease if cts the the data r=1. ext is ar ndent Supermarket Sales data from Sharpe Chapter 8 Data set Town Sales Population S-mean P-mean 1 5540456 42389-371520.2-97.1 ### 9428.41 2 10699662 57107 4787685.8 14620.9 ### ### 3 10531653 101355 4619676.8 58868.9 ### ### 4 5995282 66910 83305.8 24423.9 ### ### 5 5090095 28911-821881.2-13575.1 ### ### 6 3955072 14412-1956904.2-28074.1 ### ### 7 2773754 11081-3138222.2-31405.1 ### ### 8 4828213 25749-1083763.2-16737.1 ### ### 9 5510831 19607-401145.2-22879.1 ### ### 10 4194744 57340-1717232.2 14853.9 ### ### Mean 5911976.2 42486.1 Sum ### ### Std. Dev. ### 28399.52 ### 28399.52 (pg. 167) Correlation = Correlation 0.75 =CORREL(B3:B12,C3:C12) Sales Population Sales 1 Population 0.75 1 (S-mean) 2 (P-mean) 2 1. Cor r e pages 16 gr een an 2. Cor r e CORREL 3. Cor r e Data Ana (S-mean)*(P-mean) 36074611.42-0.14 70000275313.22 1.81 0.51 0.93 271955291571.52 1.75 2.07 3.62 2034652528.62 0.03 0.86 0.03 11157119478.12-0.31-0.48 0.15 54938324201.22-0.74-0.99 0.73 98556182013.2298556182013....
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## This note was uploaded on 06/20/2011 for the course MGMT 524 taught by Professor Andrews,r during the Spring '08 term at VCU.

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Class 3 - Linear Association - Linear Association between T...

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