If we square a feature and then apply a linear regression, it's equivalent to building a model such as.

Question

BlackTom AI · Accepted Answer

The question asks what model is equivalent to squaring a feature x and then applying linear regression. 
Option a) 'polynomial model :  y2 = a + b*x2' suggests the squared output y2 as a linear function of x2, which is not the standard form obtained from squaring the feature before regression.
Option b) 'polynomial model :  y = (a + b*x)2' implies the squared of a linear combination in x, which mixes the regression structure in a nonlinear way and does not represent a linear model in the transformed feature.
Option c) 'polynomial model :  (y = a + b*x)2' presents the square of the linear model itself, which is not how you obtain a model by simply squaring the input feature prior to regression; this form is not equivalent to regressing y on x^2.
Option d) 'polynomial model :  y = a + b*x2' expresses a linear relationship between y and x squared, i.e., a polynomial model of degree 2 in x but linear in the parameters, which is exactly what happens when you square the feature and fit a linear model: the predictor is x^2, and the regression is y = a + b*(x^2).

In summary, squaring a feature x and feeding it into a linear regression yields a model that is linear in the transformed feature x^2, with form y = a + b*(x^2). The other options misrepresent the structure either by squaring the output, squaring the entire expression, or by mixing the roles of y and the transformed feature.

If we square a feature and then apply a linear regression, it's equivalent to building a model such as.

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