ch 7 - Stat 0302B Business Statistics Spring 2010-2011...

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Stat 0302B Business Statistics Spring 2010-2011 Chapter VII Regression Analysis and Correlation § 7.1 Introduction Terminology Explanation Regression Statistical technique of modelling the relationship between variables. Linear regression Study the straight-line relationship between variables – dependent variable and independent variable(s). Simple linear regression Linear regression with only one independent variable. Predicted variable (Dependent/Response) Variable whose value is unknown and its value is predicted by values of other variables. Predictor variable (Independent/Regressor) Variable whose value is known and its value is used to predict other variables. Usually this variable is known or can be controlled and thus assumed to be fixed quantities. Example 7.1 Here are some examples of the use of simple linear regression: Dependent variable Y Independent variable X Weight Height Job performance Extent of training Returns on a stock Riskiness of the stock Mean weekly demand Price of automobile Overall GPA A-Level score Tree age (by C 14 ) Tree age (by tree rings) P.147
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Stat 0302B Business Statistics Spring 2010-2011 Scatter plot Suppose we have some randomly chosen observations of two variables, X and Y . These data can be displayed on a scatter plot: Example 7.2 The following data give the heights (in cm) and weights (in kg) for a sample of ten eighteen-year-old girls. Suppose we want to study the relationship and use the height to predict weight. The weight will be the dependent variable Y and height will be the regressor X . Height ( X ) Weight ( Y ) 169.6 71.2 164.5 58.2 165.4 56.0 168.9 64.5 162.9 53.0 160.7 52.4 163.0 56.8 163.4 49.2 161.9 55.6 173.8 77.8 The scatter plot will consist of ten points on an X-Y graph. Each point represents the datum for one girl. P.148
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Stat 0302B Business Statistics Spring 2010-2011 1. Input the data into two columns, say, column A and B . 2. ght co da A1 B11 Highli the two lumns of ta, i.e. from to . 3. Insert -> Charts -> Scatter -> Scatter with only Markers 4. The scatter plot will be created and place in the same worksheet. Use Chart Tools to formatting the graph (color, titles, fonts, scale, etc) as appropriate. The scatter plot seemingly suggests that we can summarize the relationship between the two variables by a straight line which describes the general pattern in the data. Such straight line is the main concern of the simple linear regression model. With this line, we can have a simpler understanding of the relationship between the two variables. Moreover, prediction of Y’ (a future observation) can be obtained easily through this line as long as the corresponding supplementary variable X is available. P.149
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Stat 0302B Business Statistics Spring 2010-2011 § 7.2 Correlation To understand regression, we first need to understand how to measure the relationship. Suppose we denote the X-Y data as () 1 1 , Y X , ( ) 2 2 , Y X , …, ( ) n n Y X ,, we can calculate the following summary statistics: Sample means : = X n X 1 , = Y n Y 1 Sum of squares : ( ) n X X X X S xx 2 2 2 = = , ( ) n Y Y Y Y S yy 2 2 2 = = Sum of products : ( )( ) n Y X XY Y Y X X S xy = =
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ch 7 - Stat 0302B Business Statistics Spring 2010-2011...

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