Interpreting quadratic terms in a multiple linear regression.

[Sunniva Davidson]

Hi everyone on Statalist,

I am working on a project and have run into a few obstacles.

The purpose of my project is to conduct a multiple regression analysis, with the stock price of an airline company as a dependent variable. For independent variables, I have used Oil Price, Google Trends activity, average temperature deviation in the country where the airline has most of its departures and USD/NOK exchange rate. These variables are all daily variables, and I have included all dates, even though some of the above-mentioned variables do not have values accounting for all dates, such as the weekends for oil price for example.

As Temperature Deviation, oil price (Brent) and Buzz did not fulfill the assumption of linearity, the quadratic terms of these variables were included in my multiple regression.

However, I was wondering if you could help me interpreting my results, namely the coefficients and p-values of the variables that have a quadratic term included (Brent, Buzz and TempDev)?

I would highly appreciate it!

[Carlo Lazzaro]

Sunniva:
-Brent- has a maximum in:
-Brent/2BrentSquared.
The remaining squared terms do not reach statistical significance. Hence, given the available evidence, they do not need a quadratic term.
For the future, you will be by far better off relying upon the -fvvarlist- notation to create categorical variables and interactions.

[Sunniva Davidson]

Thank you again Carlo.

However, I am a little confused. I added quadratic terms for the variables TempDev and Buzz to correct for the lack of linearity. Isn't it bad for the model to then not include the quadratic term, and do nothing to correct for the non-linear relationship with the respective independent variables and the dependent variable?

Best,

[Carlo Lazzaro]

Sunniva:
both Tempsquared and Buzzsquared do not show any evidence of non-linearity, as they are not significant.
Are you sure that you do not mean normality by linearity?

[Alfonso Sánchez-Peñalver]

Following Carlo Lazzaro's advice, I would test whether you can drop TemDevSquared Buzz and BuzzSquared

test TempDevSquared Buzz BuzzSquared

If you cannot reject the null then drop the three, and to the simpler estimation. Given your results the partial relationship between StockPrice and TempDev seems to be linear (the quadratic parameter is individually insignificant), and there seems to be no relationship with Buzz (both parameters are individually insignificant). The F test is the appropriate one to see if you drop variables, particularly since having quadratic terms in regressions is likely to inflate the standard errors due to collinearity.

[Marcos Almeida]

Just an additional note: Using marginsplot is an excellent way to a visual interpretation of squared terms.