Interpretation: coefficient for linear is negative while coefficient for squared term is positive

[Sunniva Davidson]

Hi all,

I am struggling to explain two of the variables in my regression (WeightedGT and TempDev), as they both include a squared term. The coefficient for both linear terms are negative while the squared terms are positive. How do I interpret this? Is it correct to say that the negative effect the variable has on Y will strengthen when the turning point is reached?

The WeightedGT variable measures the level of Google search activity for the company.
The TempDev is a variable of temperature deviation (how much temperature deviates from a 5 year average), hence it includes both positive and negative values. How is a variable that includes both negative and positive values interpreted in the coefficients?

I have also used marginsplot to graph their relationship, see below:

WeightedGT:



The turning point for WeightedGT was calculated at: -51,249.


Temperature deviation:



The turning point for TempDev was calculated at: -0,974.

Please excuse me if this question is rather basic, I am new to regression analysis in general.

Thank you!

[Carlo Lazzaro]

Sunniva:
you have two minima (please note that the sign of both turning points are reversed, as they should be positive).
The sign of the linear terms are consistent with the "smiling parabola" graph (for values<turning point is negatively sloped; the opposite occurs for values>turning point).

[Richard Williams]

This handout may be helpful.

https://www3.nd.edu/~rwilliam/stats2/l61.pdf