Does the following qualify as a univariate regression?

$$y=b_0+b_1x+b_2x^2+epsilon$$

I fully comprehend the implications of adding regressors and need no background information – a "yes" or "no" will do 🙂

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#### Best Answer

Yes. "Multivariate" and "univariate", when they're used to describe models, refer to the number of dependent variables, not the number of independent variables. A multivariate linear regression model, for example, predicts several different variables, and the residuals are multivariate normal rather than univariate normal. See, for example, the Wikipedia article "Linear regression":

For more than one explanatory variable, the process is called

multiple linear regression.(This term should be distinguished frommultivariate linear regression, where multiple correlated dependent variables are predicted, rather than a single scalar variable.)

Hence, your model is a multiple linear regression model, but also a univariate linear regression model.

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