Multiple Linear Regression Analysis - Reliawiki：多元线性回归分析reliawiki.ppt

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Multiple Linear Regression Analysis - Reliawiki：多元线性回归分析reliawiki.ppt

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Multiple Linear Regression Analysis - Reliawiki：多元线性回归分析reliawiki

* We’re trying to explain exam performance in terms of Revision time, previous exam performance, and difficulty of the exam. First, look at the individual shared variance between exam performance and the three predictors. Q. How do we do this? R. Pearson’s correlation. * * * * * * * * * * * * Slide * R and R2 R The correlation between the observed values of the outcome, and the values predicted by the model. R2 Yhe proportion of variance accounted for by the model. Adj. R2 An estimate of R2 in the population (shrinkage). Slide * Output: ANOVA Slide * Analysis of Variance: ANOVA The F-test looks at whether the variance explained by the model (SSM) is significantly greater than the error within the model (SSR). It tells us whether using the regression model is significantly better at predicting values of the outcome than using the mean. Slide * Output: betas Slide * How to Interpret Beta Values Beta values: the change in the outcome associated with a unit change in the predictor. Standardised beta values: tell us the same but expressed as standard deviations. Slide * Beta Values b1= 0.087. So, as advertising increases by ￡1, record sales increase by 0.087 units. b2= 3589. So, each time (per week) a song is played on radio 1 its sales increase by 3589 units. Slide * Constructing a Model Slide * Standardised Beta Values ?1= 0.523 As advertising increases by 1 standard deviation, record sales increase by 0.523 of a standard deviation. ?2= 0.546 When the number of plays on radio increases by 1 s.d. its sales increase by 0.546 standard deviations. Slide * Interpreting Standardised Betas As advertising increases by ￡485,655, record sales increase by 0.523 ? 80,699 = 42,206. If the number of plays on radio 1 per week increases by 12, record sales increase by 0.546 ? 80,699 = 44,062. Reporting the Model Slide * How well does the Model fit the data? There are two ways to assess the accuracy of the model in the sample: Residual Statistics Standardized Residuals Influential