4
$\begingroup$

I have created a linear regression model for a set of data. I have calculated the slope and intercept of the line.

If given a theoretical slope for this kind of data, how can I test to see if the slope that I calculated and the theoretical slope are significantly different?

For example, the slope I calculated is 0.02 and the theoretical slope is 0.01, are they significantly different? How can I tell? I am working in R.

$\endgroup$
2
  • 2
    $\begingroup$ By doing a one sample t-test. The regression output provides you with estimate, standard error and degrees of freedom for the observed slope and that is really all you need for a t-test. Alternatively you can use the confint function to get the confidence interval of the observed slope, $\endgroup$ – Roland Oct 16 '17 at 13:27
  • $\begingroup$ Say your variable of interest is X. Put offset(0.01 * X) and X itself into the regression equation and then test the coefficient of X or establish a confidence interval for it. @Roland suggestion works too of course. $\endgroup$ – mdewey Oct 16 '17 at 13:42
4
$\begingroup$

People are usually interested in testing if a parameter estimate is equal to $0$ because that represents no relationship. (In other contexts, 'no relationship' can be other values, such as a ratio of $1$.) However, there is no reason you need to use that specific value as your null. If you have a theoretical basis for wanting to determine if the observed slope is consistent with $.01$, you very much can use that as your null. You will just have to do that manually, since it isn't what software will output by default. The standard formula for a $t$-test is:
$$ t = \frac{(\hat\beta_j - \beta_{j\text{ NULL}})}{SE} $$ Since $\beta_{j\text{ NULL}}$ is taken by default to be $0$, that drops out and software just provides your estimate divided by the standard error. Here, you will just need to do the arithmetic yourself. Then you compare your computed $t$-statistic to the relevant $t$-distribution with the same degrees of freedom as the original test.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.