DS212_Chap12_Simple_Regression_Analysis

# DS212_Chap12_Simple_Regression_Analysis - C hapte 12: S...

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1 Chapter 12: Simple Regression Analysis And Correlation Sada Soorapanth Spring 2010

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2 Scatter plot A scatter plot showing the relationship between two variables
3 Types of relationships depicted by scatter diagrams r < 0 r > 0 r = 0

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4 Regression analysis Statistical procedure called regression analysis can be used to develop an equation showing how the variables are related. For this class, we will focus on a linear (straight line) relationship.
5 Dependent and independent variables Dependent variable (Y) is the variable being predicted. Independent variable (X) is the variable used to predict Y. Which of the following variables should be dependent and independent variables? Advertising expenditures and sales Electricity usage and daily temperatures Mortgage interest rates and home sales

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6 Linear regression equation for the population data = Predicted or estimated value of the dependent variable where β 0 = the population intercept (unknown) β 1 = the population slope (unknown) x y 1 0 ˆ β β+ = y ˆ E E ( ( y y ) ) x x Slope  Slope  1 is positive is positive Regression line Regression line Intercept Intercept 0
7 Linear regression model for the population data y = Observed value (actual data) of the dependent variable ε = Prediction error (the difference between the actual and predicted values of y) y ˆ ε β + + = x y 1 0

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8 Estimation Process y ˆ y ˆ y ˆ Sample Data: Sample Data: x        y x        y x x 1          y      y 1 .       . .       .     .       . .       .     x x n             y y n b b 0  and   and  b b 1 provide estimates of provide estimates of β 0  and   and  1 Regression Model Regression Model y = = 0 + + 1 x + + ε ε Regression Equation Regression Equation = = 0 + + 1 x Unknown Parameters Unknown Parameters b 0 , , b 1 y ˆ Estimated Estimated Regression Equation Regression Equation     =b =b 0 +b +b 1 x x Sample Statistics Sample Statistics b b 0 b b 1 y ˆ Population Sample From Anderson et al.
9 Linear regression equation of sample data x and y are sample data (observations) Regression equation: b 0 = the sample intercept b 1 = the sample slope ε = prediction error x b b y 1 0 ˆ + = Intercept (b 0 ) Slope (b 1 ) y ˆ ε + + = x b b y 1 0

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10 Least squares analysis Goal: find b 0 and b 1 to minimize the sum of squared errors
11 Formulas for computing b

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## This note was uploaded on 09/10/2011 for the course DS 212 taught by Professor Saltzman during the Spring '08 term at S.F. State.

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DS212_Chap12_Simple_Regression_Analysis - C hapte 12: S...

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