# How to interpret model diagnostics graphics after R linear regression? [closed]

I am interested in understanding the graph plots we get after running lm() command (for linear regression) in R like, for example

lm.mod1 = lm(y ~ x1 + x2)

I then get the do the summary by:

summary(lm.mod1)

I get the result as:

Residuals:
Min      1Q  Median      3Q     Max
-750.32 -160.54  -49.83  115.83 2923.74

Coefficients:
Estimate Std. Error     t value Pr(>|t|)
(Intercept)               -345.1552      37.0393   -9.319   <2e-16 ***
x1                52.9091       2.4929    21.224   <2e-16 ***
x2                8.9669        0.5395    16.620   <2e-16 ***

Residual standard error: 274.4 on 1985 degrees of freedom
Multiple R-squared: 0.2059, Adjusted R-squared: 0.2051
F-statistic: 257.3 on 2 and 1985 DF,  p-value: < 2.2e-16

I then do the plotting by

par(mfrow = c(2,2))
plot(lm.mod1)

I get 4 graphs (I can't post the graphs since I am a new user and my experience level is below 10. :/)

My questions are :

1. How do they calculate F-statistics and t-value?

2. Could someone explain me the what do we interpret with the last two graphs i.e. $\text{Scale-Location vs. (Standardized residuals)}^{1/2}$ and $\text{Residuals vs. Leverage}$. What do you mean by Leverage?

3. What do you mean by Cook's Distance? I saw it on wikipedia but I didnt get it.

4. How could we suggest if our model is a good model or not?

## closed as not a real question by onestop, Andy W, whuber♦May 23 '12 at 13:37

It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, visit the help center. If this question can be reworded to fit the rules in the help center, please edit the question.

• I answered many of these questions last week. You will learn more if you search for similar questions from other sources. – gregmacfarlane May 22 '12 at 21:04
• An even better discussion here: stats.stackexchange.com/questions/5135/… – gregmacfarlane May 22 '12 at 21:06
• These are good questions, but as the comments and attempted replies indicate, they cover too much ground. Please focus on one at a time, perform some research, and be specific about what you're looking for. "I didn't get it" doesn't give us enough clues to provide the information you need. – whuber May 23 '12 at 13:37

I rarely do this, but your question is so general, and covers so many topics, that I don't see any other choice than to point you to something like this:

http://cran.r-project.org/doc/contrib/Faraway-PRA.pdf

And tell you to simply read.

There is a newer version for this book here:

http://www.amazon.com/Linear-Models-Chapman-Statistical-Science/dp/1584884258/

• For some great books on regression diagnostics there is the book from the 1980s by Belsey, Kuh and Welsch (published by Wiley) Somewhat later Dennis Cook published some regression books that emphasize graphics and regression diagnostic including his own Cook's distance. These books tended to cover concept and not specific software. This was way before the R revolution and some even before S became popular. – Michael Chernick May 22 '12 at 21:31

As @TalGalili said .... you need to read a good book on regression. Faraway's book is fine. There are many other good ones. One that I like, that is R-specific, and has a new edition is by Fox and Weisberg. A more general and somewhat more advanced book is Frank Harrell's Regression Modeling Strategies, which also uses R.

• Hi Peter. Regression Modeling Strategies is great, but would you send a novice to it?! :) Fox's book is also a good suggestion! – Tal Galili May 23 '12 at 6:15
• Hi @TalGalili you're right, RMS is not for novices. I did say "more advanced" but perhaps I shouldn't even have mentioned it in this context. – Peter Flom May 23 '12 at 10:01