Regression and ANOVA

Regression and ANOVA - Statistics 101 Regression and ANOVA...

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Statistics 101 Regression and ANOVA Week 9 Fall 2007 Professor Esfandiari The objective of this lecture is to provide you with some guidelines that could be potentially useful for your project Compare simple linear regression and two sample test of the mean Compare one-way ANOVA and multiple linear regression Compare ANOVA and regression Show you when you can use each method Provide you with simple examples of both I Comparing two-sample test of the mean and simple linear regression We used two-sample test of the mean to compare the mean of two independent populations. The null hypothesis as: H0: μ 1 - μ 2 = 0 In simple linear regression the null hypothesis that we test is that the slope of the regression line is equal to zero; H0: β = 0 Example: Do ninth grade boys and girls feel equally safe in high school? Here is the results for the two-sample test of the mean. Fail to reject the null. Group Statistics GENDER N Mean Std. Deviation Std. Error Mean posttest on school safety male 241 48. 03 21.103 1.359 female 236 46.93 19.292 1.256 Independent Samples Test Levene's Test for Equality of Variances t-test for Equality of Means F Sig. t df Sig. (2- tailed) Mean Difference Std. Error Difference 95% Confidenc e Interval of the Difference Lower posttest on school safety Equal variances assumed .510 .475 .594 475 .553 1.10 1.852 -2.539 Equal variances .595 472.779 .552 1.10 1.851 -2.535 1
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not Now we will use simple linear regression to do the same analysis Click on analyze Click on regression Enter safety2 in the dependent box Enter gender in the independent box and click on OK You have to make sure that gender is dummy coded to zero and one. Variables Entered/Removed Model Variables Entered Variables Removed Method 1 GENDER . Enter a All requested variables entered. b Dependent Variable: posttest on school safety Model Summary Model R R SquareAdjusted R Square Std. Error of the Estimate 1 .027 .001 -.001 20.227 a Predictors: (Constant), GENDER ANOVA Model Sum of Squares df Mean Square F Sig. 1 Regressio n 144.560 1 144.560 .353 .553 Residual 194336.57 2 475 409.130 Total 194481.13 2 476 a Predictors: (Constant), GENDER b Dependent Variable: posttest on school safety Coefficients Unstandar dized Coefficient s Standardiz ed Coefficient s t Sig. Model B Std. Error Beta 1 (Constant) 48.029 1.303 36.862 .000 GENDER -1.101 1.852 -.027 -.594 .553 a Dependent Variable: posttest on school safety 2
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Comparison of the printouts for the two-sample test of the mean and the printout for simple linear regression Notice that the t values are the same (0.594) In both cases you fail to reject the null. F = t squared Slope or -1.01 is the same as the difference between the two means SLR gives you R squared while the two-sample test of the mean does not. Interpretation of slope as we go from
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Regression and ANOVA - Statistics 101 Regression and ANOVA...

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