There are many situations where we might be interested in creating a new variable by transforming one of the variables already in the data frame. The **R** programming language can be used for either simple transformations or more complicated mathematical expressions where necessary.

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There are many situations where the logarithmic scale is used for data and if we have data on its original scale then we can use the **log** function in **R** to create a new variable. The default base for the **log** function is the natural logarithm. Referring back to the olive oil data set used in previous posts if we wanted to create a new variable that is the logarithm of one of the numeric variables then we could use code such as:

log(olive.df$palmitic) |

which produces the following output:

[1] 6.980076 6.992096 6.814543 6.873164 6.957497 6.814543 6.826545 7.003065 6.986566 6.944087 [11] 6.957497 6.943122 6.979145 6.774224 6.858565 7.051856 6.849066 7.153052 6.867974 6.858565 [21] 6.979145 6.902743 6.962243 6.970730 6.970730 7.181592 7.186144 7.214504 7.228388 7.166266 ... |

If we had wanted to to take the square root of this variable instead we would use the **sqrt** function:

sqrt(olive.df$palmitic) |

and the output would be:

[1] 32.78719 32.98485 30.18278 31.08054 32.41913 30.18278 30.36445 33.16625 32.89377 32.20248 [11] 32.41913 32.18695 32.77194 29.58040 30.85450 33.98529 30.70831 35.74913 31.00000 30.85450 [21] 32.77194 31.54362 32.49615 32.63434 32.63434 36.26293 36.34556 36.86462 37.12142 35.98611 ... |

It is possible to create more complicated expressions based on different transformations using the **R** programming language.

For example we might want to *centre* a vector of data by removing the mean value for the data and scale to unit variance. Based on the palmitic variable used in the previous examples we could use the **scale** function to perform this operation:

> scale(olive.df$palmitic) [,1] [1,] -0.92970611 [2,] -0.85259700 [3,] -1.90246724 ... [571,] -1.43388109 [572,] -1.61182519 attr(,"scaled:center") [1] 1231.741 attr(,"scaled:scale") [1] 168.5923 |

The mean and standard deviations used for the scaling are saved as attributes by the function.