CSC 121, Spring 2017, Large Assignment #2, Part 1 script.

We'll see how well Zipf's Law applies to Jane Ausin's “Pride and Prejudice”.

```
> source("lga2-defs1.R")
>
> text <-
+ scan("http://www.cs.utoronto.ca/~radford/csc121/pride-and-prejudice.txt","")
```

Find the counts for each unique word, and sort them to go with ranks of 1, 2, 3, …

```
> word_counts <- sort(table(text),decreasing=TRUE)
> word_ranks <- 1:length(word_counts)
```

Plot the counts versus ranks for the whole set of words, on logarithmic scales, along with the best fit line, as found by 'lm'.

```
> # First, create an empty plot with the right scales.
>
> plot (log(word_ranks), log(word_counts),
+ xlab="log word rank", ylab="log word count",
+ type="n")
>
> # Add the points and best fit line, and save the result of 'lm' in 'm'.
>
> m <- plot_with_line (log(word_ranks), log(word_counts)) # from lga2-defs1.R
```

Here are the parameters of the best fit line for all words.

```
> coef (m)
```

```
(Intercept) x
11.700 -1.355
```

The line does not fit the points very well, and has a slope that is not very close to the slope of -1 expected for the original form of Zipf's Law.

Based on the plot above, it seems like the words the 20 highest ranks are best modelled separately, and the the words with ranks above 700 are also best modelled separately. Here is the plot of these three groups, with separately fitted lines.

```
> # Create an empty plot with the right scales.
>
> plot (log(word_ranks), log(word_counts),
+ xlab="log word rank", ylab="log word count",
+ type="n")
>
> # Add points and best fit lines for each of the three groups, in different
> # colours.
>
> w1 <- 1:20
> m1 <- plot_with_line (log(word_ranks[w1]), log(word_counts[w1]),"orange")
>
> w2 <- 21:700
> m2 <- plot_with_line (log(word_ranks[w2]), log(word_counts[w2]),"green")
>
> w3 <- 701:length(word_counts)
> m3 <- plot_with_line (log(word_ranks[w3]), log(word_counts[w3]),"blue")
```

Here are the parameters of the lines for the three groups.

```
> rbind (coef(m1), coef(m2), coef(m3))
```

```
(Intercept) x
[1,] 8.627 -0.5259
[2,] 10.311 -1.1156
[3,] 13.141 -1.5334
```

The fit of the lines to the points is much better when the words are divided into three groups. The slope for the middle group of -1.1 is close to the slope of -1 that would be expected for the original form of Zipf's Law.