Modeling fish

Introduction

Goal

Practice modeling using the fish dataset on two common fish species in fish market sales.

Packages

We will use the tidyverse package for data wrangling and visualization and the tidymodels package for modeling.

Data

These data come from Kaggle and is commonly used in machine learning examples.

fish <- read_csv("https://data-science-with-r.github.io/data/fish.csv")

The data dictionary is below:

variable description
species Species name of fish
weight Weight, in grams
length_vertical Vertical length, in cm
length_diagonal Diagonal length, in cm
length_cross Cross length, in cm
height Height, in cm
width Diagonal width, in cm

Let’s take a look at the data.

fish
# A tibble: 55 × 7
   species weight length_vertical length_diagonal length_cross height width
   <chr>    <dbl>           <dbl>           <dbl>        <dbl>  <dbl> <dbl>
 1 Bream      242            23.2            25.4         30     11.5  4.02
 2 Bream      290            24              26.3         31.2   12.5  4.31
 3 Bream      340            23.9            26.5         31.1   12.4  4.70
 4 Bream      363            26.3            29           33.5   12.7  4.46
 5 Bream      430            26.5            29           34     12.4  5.13
 6 Bream      450            26.8            29.7         34.7   13.6  4.93
 7 Bream      500            26.8            29.7         34.5   14.2  5.28
 8 Bream      390            27.6            30           35     12.7  4.69
 9 Bream      450            27.6            30           35.1   14.0  4.84
10 Bream      500            28.5            30.7         36.2   14.2  4.96
# ℹ 45 more rows

Analysis

Visualizing the model

We’re going to investigate the relationship between the weights and heights of fish, predicting weight from height.

  • Create an appropriate plot to investigate this relationship. Add appropriate labels to the plot.
# add code here
  • If you were to draw a a straight line to best represent the relationship between the heights and weights of fish, where would it go? Why?

Add response here.

# add code here
  • What types of questions can this plot help answer?

Add response here.

  • We can use this line to make predictions. Predict what you think the weight of a fish would be with a height of 10 cm, 15 cm, and 20 cm. Which prediction is considered extrapolation?

Add response here.

  • What is a residual?

Add response here.

Model fitting

  • Fit a model to predict fish weights from their heights.
# add code here
  • Predict what the weight of a fish would be with a height of 10 cm, 15 cm, and 20 cm using this model.
# add code here
  • Calculate predicted weights for all fish in the data and visualize the residuals under this model.
# add code here

Model summary

  • Display the model summary including estimates for the slope and intercept along with measurements of uncertainty around them. Show how you can extract these values from the model output.
# add code here
  • Write out your model using mathematical notation.

Add response here.

Correlation

We can also assess correlation between two quantitative variables.

  • What is correlation? What are values correlation can take?

Add response here.

# add code here

Adding a third variable

  • Does the relationship between heights and weights of fish change if we take into consideration species? Plot two separate straight lines for the Bream and Roach species.
# add code here

Fitting other models

  • We can fit more models than just a straight line. Use method = "loess". What is different from the plot created before?
# add code here