# Is a regression estimator consistent without an intercept

Statistics pp 459-496 | Cite as

- Ludwig Fahrmeir
- Rita artist
- Iris Pigeot
- Gerhard Tutz

### Summary

Section 3.6 deals with how the influence of an explanatory feature *X* on a target feature *Y* can be represented and exploratively investigated. Both features are assumed to be scaled metrically, and it is assumed that the relationship between *Y* and *X* can be described by an approximate relation of the form \ (Y = f (X) + \ varepsilon \). It is *f* a deterministic regression function and *ε* a bug caused by *X* alone cannot be explained. The best known is the linear single regression, in which a linear regression function \ ([f = (X) = \ alpha + \ beta X \) is used as the “best-fit line”. We also consider the CAP model as an example in this chapter *Y* = “Stock return minus interest” and *X* = “Market return” and the rent index regression with *Y* = “Net rent” (or “net rent / sqm”) and *X* = “Living space”. Figures 3.17 and 3.20 from Section 3.6 show the scatter diagrams and the associated best-fit line.

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### Authors and Affiliations

- Ludwig Fahrmeir
- Rita artist
- Iris Pigeot
- Gerhard Tutz

- 1. Institute for Statistics, University of Munich, Munich, Germany
- 2. Institute for Statistics, University of Munich, Munich, Germany

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