I used the inbuilt dataset stackloss here. I used following R code for creating the multiple regression model.

> head(stackloss)
  Air.Flow Water.Temp Acid.Conc. stack.loss
  1        80         27         89         42
  2        80         27         88         37
  3        75         25         90         37
  4        62         24         87         28
  5        62         22         87         18
  6        62         23         87         18

> fit <- lm(stack.loss ~ .,data=stackloss)
> plot(fit)

And when I plot the model, the four following graphs are displayed. Graph-1 Graph-2 Graph-3 Graph-4

How to interpret these graphs? What are the significance of these graphs? How to use these graphs?

  • $\begingroup$ If you are interested in plotting your estimates or effect plots, you may look at the sjPlot-Package (see some examples here. $\endgroup$
    – Daniel
    Commented Nov 16, 2015 at 8:13

1 Answer 1


These plots are are model diagnostics. Generally, you wouldn't include any of these in a final manuscript, but they are essential to checking the model's assumptions.

The first plot plots the residuals against the values predicted by the model; it is useful for identifying outliers, poor fit, and heteroskedasticity. The third plot is essentially the same, with residuals scaled to have a variance of 1 and then square-root transformed.

The second plot is a normal Q-Q plot, which can help detect deviations from normality. In essence, the closer the points lie to the line, the better it meets the normality assumption.

The fourth plot looks at the effect of leverage (how much each given predictor affects the fit; essentially, outliers in the x-variables). The dotted lines represent Cook's distance, which is the degree to which the regression would change if a data point were removed. In this case, it looks like point 21 may be problematic.

Greater detail on interpreting these plots can be found here.


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