Lecture 6_Multiple regression B

# Lecture 6_Multiple regression B - 1 ECON1320 Quantitative...

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Unformatted text preview: 1 ECON1320 Quantitative Economics and Business Analysis B LECTURE 6 Multiple Regression B Chapter 13.3, 15.4, 16.5, 15.2 Today’s topics c Assumptions of the MR model c Assessing the assumptions 1. Linearity in the relationship between Y and X i 2. Normality of error terms ( ε ) 3. Homoscedasticity 4. Independence of error terms 5. Independence of explanatory variables c Indicator (dummy) variables in the MR model Assumptions of linear regression 1. Linearity (check by Y-X plots or residual plot) Error Term ( ε ) Assumptions : 2. Normality of Error: Error values ( ε ) are a random variable, normally distributed for any given value of X, with mean zero ( μ ε =0). 3. Homoscedasticity: The probability distribution of the errors ( ε ) has constant variance ( σ 2 ) 4. Independence of Errors: Error values are statistically independent i.e. not correlated. Independent variables Assumption : 5. No collinearity The independent variables are not correlated. Assumption 1: Linearity- Residual analysis Not Linear Linear C x residuals x Y x Y x residuals Non-linearity 100 200 300 400 500 600 700 800 900 1980 1985 1990 1995 2000 2005 50 100 150 200 250 300 350 400 450 1980 1985 1990 1995 2000 2005 Example 1 c Use data for Auto2002.xls to predict fuel consumption (Y) from length (X 1 ), width (X 2 ), weight (X 3 ) and horsepower (X 4 ) Y = β + β 1 X 1 + β 2 X 2 + β 3 X 3 + β 4 X 4 + ε c Data Analysis: Tools/Data Analysis/Regression/… Tick Residuals, Residual plots & Normal probability plot c KaddStat: Kadd/Regression and Correlation/Simple/Multiple… Tick Residual Plots c PhStat/Regression/MultipleRegression T ick Residuals Table and Residuals Plot 2 Excel output 0.0040-0.0296 0.1347-1.5064 0.0085-0.0128 Horse power-0.0033-0.0058 0.0000-7.0951 0.0006-0.0045 Weight 0.3314-0.3899 0.8727-0.1606 0.1821-0.0292 Width 0.0825-0.0656 0.8214 0.2263 0.0374 0.0085 Length 56.4269 23.3665 0.0000 4.7804 8.3460 39.8967 Intercept Upper Lower 95% P-value t Stat Stan.Error Coefficients 2627.2893 120 Total 8.6233 1000.3001 116 Residual 0.0000 47.1685 406.7473 1626.9891 4 Regression Signi. F F MS SS df ANOVA 121 Observations 2.9365 Standard Error 0.6061 Adjusted R 2 0.6193 R Square 0.7869 Multiple R Regression Statistics Some observations c F-test is significant at the 5% level b there is a relationship between petrol assumption and length, weight, height & horse power variables. c T-test for Weight is significant at the 5% & this is the only significant t-test. c The sign of Length coefficient is theoretically “wrong”. c R square and adjusted R square is not small. c b we need to assess the violation of the assumptions of the estimated model. Assessing Assumption 1: Linearity -10.0000-5.0000 0.0000 5.0000 10.0000 15.0000 20.0000 20 40 60 80 100 120 140 Observations Residuals C Assumption 2- Normality of error Y = β + β 1 X 1 + β 2 X 2 +…+ β k X k + ε mean zero ( μ ε =0) implies that for given values of X 1 , X 2 , …, and X k the expected (average) value of Y is given by...
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Lecture 6_Multiple regression B - 1 ECON1320 Quantitative...

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