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.

View Explanation

Log in for full answers

Similar Questions

The most common functional form that is nonlinear in the variables is the _______ form.

When fitting a linear model with polynomial basis functions, which of the following has no impact on the model complexity?

In the context of polynomial regression models, which of the following statements are true about the coefficient of determination (R²)? Select all that apply.

Now, add stotal2 to the equation you estimated in Question 14. Does a quadratic in the test score variable stotal seem necessary?

Consider m-th order polynomial regression. Which of the the following statements are true? [Select ALL that apply.]

In a consumer society, many adults channel creativity into buying things

Economic stress and unpredictable times have resulted in a booming industry for self-help products

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler