statistically significant; p-value; t-stat

#1
I have a dataset that produced the following for a second-order polynomial:


1st order (linear) coefficient: 1.1089994
1st order (linear) standard error: 0.0103303
2nd order (nonlinear) Coefficient: -0.0020471
2nd order (nonlinear) standard error: 0.0001306
t-stat: -15.7
p-value: 1.04E-06
Student's t: 2.201


Regarding the 2nd order coefficient:
As you can see the p-value is less than 0.05 and the absolute value of the t-stat is greater than the Student's t, which implies that the nonlinear coefficient is considered to be statistically significant. However, the coefficient is really small, i.e. NOT significantly different than zero, especially when compared to the 1st order coefficient. Based on these results can I consider the dataset linear?

Thanks
 

JohnM

TS Contributor
#2
Based on the 2nd order standard error, it looks like the 2nd order coefficient is actually significantly different from 0.....and based on these numbers alone, I would say no, the dataset is not linear.

Did you try to graph it?
 
#3
Thanks so much for your response. I just don't understand how such small numbers for both coefficient and standard error can lead to the coefficient being considered significant.
 

JohnM

TS Contributor
#4
Don't confuse "significant" with "large" or "important." Significant just means that it is larger than what could be explainable by chance or random outcome alone.