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For some consecutive years I have a number of incidents in a given city. From the scatter plot I deducted that the incidents increase linearly, so I performed a Linear Regression test. The slope is about 30 degrees.

Is there a way to show that this line is increasing in time?

I guess I have to compare the slope of my line with an imaginary horizontal line (zero degrees slope).

I have found this Q&A: Test a significant difference between two slope values. In my problem, the standard errors I have are zero for both lines.

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    $\begingroup$ Correct me if I misunderstood you, but when you perform linear regression, and your slope coefficient has p-value < 0.05, it means it is signifficantly different of 0. In another words, you already know that there is effect of "time" (in your case) in the response variable, and as this slope coefficient is positive, it means y is INCREASING over time. $\endgroup$ – Bruna w Dec 1 '17 at 14:25
  • $\begingroup$ Could you please provide the output of your regression? I'm not sure what do you mean about of SE = 0 because t coefficient is calculated as t= estimator coefficient/standard error $\endgroup$ – Alejandro Carrera Dec 1 '17 at 14:48
  • $\begingroup$ @Brunaw for Linear Regression, p < 0.05 means that my data can be interpreted well by the y=ax +b equation. Am I wrong? $\endgroup$ – AchiPapakon Dec 1 '17 at 15:10
  • $\begingroup$ @Aquilles Not really. For linear regression, you're testing the effect of the explanatory variables on the response. If you have a p-value < 0.05 for one variable, it means that its effect on the response is different of 0. And the magnitude of the effect of this explanatory variable is given by its coefficient :) $\endgroup$ – Bruna w Dec 1 '17 at 15:17
  • $\begingroup$ @Brunaw well explained. On the contrary, p >= 0.05 for the slope coefficient means y = 0 + b (steady over time). And p >= 0.05 for both means y = 0 or Linear Regression is not applicable? $\endgroup$ – AchiPapakon Dec 1 '17 at 15:40