stacklossmreg lmstackloss AirFlow WaterTemp AcidConc summ

> stackloss.mreg = lm(stack.loss~ Air.Flow +Water.Temp+ Acid.Conc.) > summary(stackloss.mreg) Call:lm(formula = stack.loss - Air.Flow + Water.Temp + Acid.Cone.) Residuals: Residual standard error: 3.243 on 17 degrees of freedom Multiple R-squared: 0.9136, Adjusted R-squared: 0.8983 F-statistic: 59.9 on 3 and 17 OF, p-value: 3.016e-09

Solution

Linearity Assumption: (is violated)

When considering a simple linear regression model, it is important to check the linearity assumption -- i.e., that the conditional means of the response variable are a linear function of the predictor variable. Graphing the response variable vs the predictor can often give a good idea of whether or not this is true. However, one or both of the following refinements may be needed:

1. Plot residuals (instead of response) vs. predictor. A non-random pattern suggests that a simple linear model is not appropriate; you may need to transform the response or predictor, or add a quadratic or higher term to the mode.

2. Use a scatterplot smoother such as lowess (also known as loess) to give a visual estimation of the conditional mean. Such smoothers are available in many regression software packages. Caution: You may need to choose a value of a smoothness parameter. Making it too large will oversmooth; making it too small will not smooth enough.