# Multiple Linear Regression with 2 predictors

I have a set of data and supposed to see if the linear model $$Y=\beta_0 + \beta_1 X_1 + \beta_2X_2 + \varepsilon$$ fits the data (mydata, using R) below is a scatter plot.

> mydata=read.table(....)
> pairs(mydata)


I am not very good at interpreting scatter plots(yet). From the output, how can i tell whether the model fits? thanks

• You can't tell visually, but you can get some hints. Right away you can see that the relationship between $Y$ and both $X$ variables is non-linear. This is an indication you might want to log-transform the variables. – gregmacfarlane Apr 4 '13 at 15:31
• thanks. yes, i am contemplating this non-linear behaviour. can i sa y that if its non-linear, then the data won't fit? (before the log transform) thanks. Or should i say that we cannot decide until we log transform it ? thanks – dorothy Apr 4 '13 at 15:38
• It lloks like you have some outliers in your data: you may want to remove this and have a second look at the scatterplots. Besides that, I would be careful drawing conclusions from 2D-plots for a 3D analysis... – Nick Sabbe Apr 4 '13 at 15:52
• The easiest way to "justify" the failure of a model would be by showing that your residuals are not Gaussian; $N(0,\sigma^2)$. That would violate the assumption of normality and justify the transformation of your data (maybe all of them, maybe some of them). While there are indication that "the data won't fit" just showing a scatter plot of the data is not sufficient. BTW, check if square of your predictors do a slightly better job and think what is the physical meaning of your logged predictors for example. – usεr11852 Apr 4 '13 at 15:59
• You really can't say anything until you model it. – gregmacfarlane Apr 4 '13 at 16:11