# Software tutorial/Transformation of data in a linear model

From Statistics for Engineering

This is shown by example for a few different types of transformations:

Description | Desired model | Formula function in R |
---|---|---|

Fit only an intercept | \(y = b_0\) | `lm(y ~ 1)` the character is a "one" |

Standard, univariate model | \(y = b_0 + b_1 x\) | `lm(y ~ x)` |

Force intercept to zero (check the degrees of freedom!) | \(y = b_1 x\) | `lm(y ~ x + 0)` |

Transformation of an \(x\) | \(y = b_0 + b_1\sqrt{x}\) | `lm(y ~ sqrt(x))` |

Transformation of \(y\) | \(\log(y) = b_0 + b_1 x\) | `lm(log(y) ~ x)` |

Transformation of \(y\) | \(100/y= b_0 + b_1 x\) | `lm(100/y ~ x)` |

Transformation of \(x\): +, -, /, and ^ do not work on the right hand side! |
\(y= b_0 + \dfrac{b_1}{x}\) | `lm(y ~ 1/x)` will work, but is not doing what you expect. It is fitting a model \(y = b_0\)!! Be careful. |

Most transformations of \(x\) must be wrapped in an AsIs `I()` operation: |
\(y= b_0 + \dfrac{b_1}{x}\) | `lm(y ~ I(1/x))` will work as expected |

Another use of the AsIs `I()` operation |
\(y= b_0 + b_1 x^2\) | `lm(y ~ I(x^2))` |

Another use of the AsIs `I()` operation |
\(y= b_0 + b_1 (x - \bar{x})\) | `lm(y ~ I(x - mean(x)))` |