# Multiple Linear Regression Model with independent Variable as a linear Function of itself

Does anyone of you know what happens to the b coefficients and to R-squared when a dependent variable is expressed as a linear function of itself in a multiple regression as

$$y = b_0 + b_1x_{1}^* + b_2x_2 + \cdots + b_kx_k + u,$$

when, suppose,

$$x_{1}^* = a + cx_1$$ Where a and c are given coefficients.

What is the difference between this model and the usual model

$$y = b_0 + b_1x_{1}^* + b_2x_2 + \cdots + b_kx_k + u$$

• This sounds like you are describing a certain special type of what is usually called an "errors-in-variables" model. Have you read anything about those? See the wikipedia article, for instance: en.wikipedia.org/wiki/Errors-in-variables_models Apr 12 '18 at 12:24
• I think there might be a couple typos. In the first paragraph, you say "dependent variable," but the rest of the question is about an independent variable. Also, should the x1* in the "usual model" be just x1? Apr 12 '18 at 12:30