# [R] lm without intercept

citynorman citynorman at hotmail.com
Sat Jul 28 19:40:18 CEST 2012

```I've just picked up R (been using Matlab, Eviews etc) and I'm having the same
issue. Running reg=lm(ticker1~ticker2)  gives R^2=50% while running
reg=lm(ticker1~0+ticker2) gives R^2=99%!! The charts suggest the fit is
worse not better and indeed Eviews/Excel/Matlab all say R^2=15% with
intercept=0. How come R calculates a totally different value?!

Call:
lm(formula = ticker1 ~ ticker2)

Residuals:
Min       1Q   Median       3Q      Max
-0.22441 -0.03380  0.01099  0.04891  0.16688

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept)  1.57062    0.08187   19.18   <2e-16 ***
ticker2      0.61722    0.02699   22.87   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.07754 on 530 degrees of freedom
Multiple R-squared: 0.4967,	Adjusted R-squared: 0.4958
F-statistic: 523.1 on 1 and 530 DF,  p-value: < 2.2e-16

Call:
lm(formula = ticker1 ~ 0 + ticker2)

Residuals:
Min        1Q    Median        3Q       Max
-0.270785 -0.069280 -0.007945  0.087340  0.268786

Coefficients:
Estimate Std. Error t value Pr(>|t|)
ticker2 1.134508   0.001441   787.2   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.1008 on 531 degrees of freedom
Multiple R-squared: 0.9991,	Adjusted R-squared: 0.9991
F-statistic: 6.197e+05 on 1 and 531 DF,  p-value: < 2.2e-16

Jan private wrote
>
> Hi,
>
> thanks for your help. I'm beginning to understand things better.
>
>> If you plotted your data, you would realize that whether you fit the
>> 'best' least squares model or one with a zero intercept, the fit is
>> not going to be very good
>> Do the data cluster tightly around the dashed line?
> No, and that is why I asked the question. The plotted fit doesn't look
> any better with or without intercept, so I was surprised that the
> R-value etc. indicated an excellent regression (which I now understood
> is the wrong interpretation).
>
> One of the references you googled suggests that intercepts should never
> be omitted. Is this true even if I know that the physical reality behind
> the numbers suggests an intercept of zero?
>
> Thanks,
> 	Jan
>
> ______________________________________________
> R-help@ mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>

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