AE 10: Modelling fish

Application exercise

For this application exercise, we will work with data on fish. The dataset we will use, called fish, is on two common fish species in fish market sales.

import pandas as pd
import seaborn as sns
import matplotlib.pyplot as plt
from sklearn.linear_model import LinearRegression
import numpy as np

fish = pd.read_csv("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

Visualizing the model

We’re going to investigate the relationship between the weights and heights of fish.

Create an appropriate plot to investigate this relationship. Add appropriate labels to the plot.

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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?

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- Now, let Python draw the line for you. Refer to the documentation at https://seaborn.pydata.org/generated/seaborn.lmplot.html. Specifically, refer to the method section.
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- What types of questions can this plot help answer?
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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.

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Predict what the weight of a fish would be with a height of 10 cm, 15 cm, and 20 cm using this model.

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Calculate predicted weights for all fish in the data and visualize the residuals under this model.

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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.

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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?

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- Are you good at guessing correlation? Give it a try! https://www.rossmanchance.com/applets/2021/guesscorrelation/GuessCorrelation.html
What is the correlation between heights and weights of fish?

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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.

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Fitting other models

We can fit more models than just a straight line. Change the sns.regplot() code you previously used to include lowess=True. What is different from the plot created before?

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