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Results tagged with linear
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user 22228
For statistical topics which involve the assumption of linearity, for example, linear regression or linear mixed models, or for the discussion of linear algebra as applied to statistics.
10
votes
Pearson correlation between a variable and its square
The high $r$ is not telling you that the relationship is linear, but it is telling you that the relationship is rather close to being linear. … Moreover, we can see from our table of output from the corn function that increasing the value of $n$ makes the linear correlation smaller (note that with two points, we had a perfect linear fit and a …
- 23.9k
37
votes
Accepted
In multiple linear regression, why does a plot of predicted points not lie in a straight line?
The relationship between $\hat y$ and $x_1$ is linear when $x_2$ is controlled for (i.e. for constant $x_2$, the relationship between $\hat y$ and $x_1$ is a straight line), which is often described as …
- 23.9k
8
votes
Accepted
Why does the sum of residuals equal 0 from a graphical perspective?
Note that setting the coefficient of the linear term in the change to zero (which we did by getting the red and blue rectangles to cancel out) is equivalent to putting $f'(a)=0$, i.e. ensuring the point …
- 23.9k
6
votes
Linear regression - is a model "useless" if $R^2$ is very small?
If your model is correctly specified and the appropriate conditions for your inference method are satisfied (e.g. i.i.d. Gaussian errors if you want to use a t-test), then you should be able to achiev …
- 23.9k