anova2_2page - ANOVA II March 7 2007 Prediction of new...

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ANOVA II March 7, 2007 Prediction of new outcomes Predictions can be made with any linear model, either regression or ANOVA Let’s illustrate with the electricity usage data t = a value of temperature usage ( t ) = β 0 + β 1 t + β 2 t 2 = electricity usage in some future month with average temperature t the predicted value of usage ( t ) is usage ( t ) = β 0 + β 1 t + β 2 t 2
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Confidence and prediction intervals for new outcomes From previous page: usage ( t ) = β 0 + β 1 t + β 2 t 2 usage ( t ) estimates both usage ( t ) = β 0 + β 1 t + β 2 t 2 + and E { usage ( t ) } = β 0 + β 1 t + β 2 t 2 prediction intervals for β 0 + β 1 t + β 2 t 2 + are wider than confidence intervals for β 0 + β 1 t + β 2 t 2 because of extra uncertainty due to Sinusoidal model For forecasting: a better model has only month of the year as a predictor
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R code – using sinusoidal model eldata <- read.table(’elec_usage.txt’,header=TRUE) eldata.lm <- lm(usage~sin(pi*month/6)+cos(pi*month/6),data=eldata) new = data.frame(month = seq(1,12,1)) pred.plim <- predict.lm(eldata.lm, new, interval="prediction") pred.clim <- predict.lm(eldata.lm, new, interval="confidence") pdf(’electricity_sine_prediction.pdf’) matplot(new$month,cbind(pred.clim, pred.plim[,-1]),
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