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How to test the statistical significance of the difference between two Linear Regression slopes?

There are two time-series: T1 and T2. They come from different studies and mean different things. On T1 we do a Linear Regression and get the coefficient B1. On T2 we do a Linear Regression and get the coefficient B2.

  1. For comparison of the slopes, do I need the dependant variable to be the same?
  2. Can time be this dependant variable?
  3. What are the recommended statistical tests to apply in this case? T-test?

Thank you for your time!

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  • $\begingroup$ Please give more context so someone can provide a helpful answer. Obviously, if the two slopes are measured in different units then it doesn't make sense to compare their numerical value. You can't compare a slope that is expressed as miles per gallon with another slope that is inches per year. $\endgroup$
    – Harvey Motulsky
    Mar 15 at 15:48

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  1. I am not sure what do you mean by "comparison of the slopes", because if you have just two models, you would get just two slopes: let's say: a1 and a2. Then how would you like to test the statistical significance of the differences between just these two?

Anyway, if you would like to compare two models, it would be helpful that the dependent variable is the same in both models. This way you would be able to show, e.g., that the model no. 1 is better than model no. 2 because (even though different independent variables were used), the model no. 1 allows for a better prediction of the values the dependent variable takes. See my question: Statistical significance of the difference between two regression models

  1. As far as I understand, in time-series models, time is an independent variable (usually denoted as "X"). I.e., given time (and optionally some other parameters), you attempt to predict the values of the dependent variable (usually denoted as "Y"). I.e. your output value depends on time (or at least that is that you hope for to show). More on the difference between independent and dependent variables: https://www.scribbr.com/methodology/independent-and-dependent-variables/ ; and: https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-equations-and-inequalities/cc-6th-dependent-independent/a/dependent-and-independent-variables-review

  2. As I stated before, I am not completely sure what did you mean in points 1. and 2. , but generally, yes, I would use a t-test, see my question: Statistical significance of the difference between two regression models

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