Homework 6: Linear Regression

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Homework 6: Linear Regression#

Apply linear regression to predict chemical process outcomes.

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from sklearn.linear_model import LinearRegression
from sklearn.model_selection import train_test_split
from sklearn.metrics import mean_squared_error, r2_score
from sklearn.preprocessing import StandardScaler

Problem 1: Simple Linear Regression#

You have data relating reaction temperature to product purity.

# Load simple regression data from URL
url = "https://raw.githubusercontent.com/jkitchin/s26-06642/main/dsmles/data/hw06_simple_regression.csv"
simple_data = pd.read_csv(url)
temperature = simple_data['temperature'].values
purity = simple_data['purity'].values

1a. Fit a linear regression model. Report the intercept and slope.

# Your code here

1b. Plot the data and the fitted line. Include proper labels and title.

# Your code here

1c. What purity would you predict at 500 K? Is this prediction reliable? Why or why not?

# Your code here

Problem 2: Multiple Linear Regression#

Predict reaction yield from multiple process variables.

# Load multiple regression data from URL
url = "https://raw.githubusercontent.com/jkitchin/s26-06642/main/dsmles/data/hw06_multiple_regression.csv"
data = pd.read_csv(url)
data.head()
temperature pressure catalyst_loading residence_time yield
0 374.908024 1.282863 3.389142 12.584086 54.693902
1 490.142861 6.727694 0.878630 36.567732 67.896154
2 446.398788 3.829204 1.227329 37.031756 61.590318
3 419.731697 5.577136 4.543494 41.871495 77.475560
4 331.203728 9.168098 3.228931 46.304567 72.465092

2a. Split the data into 80% training and 20% test sets. Fit a multiple linear regression model.

# Your code here

2b. Report the R² score for both training and test sets. Is there evidence of overfitting?

# Your code here

2c. Calculate standardized coefficients. Which variable has the largest effect on yield?

# Your code here

2d. Create a residual plot. Does the model appear adequate?

# Your code here

Problem 3: Interpretation#

3a. Based on your model, if you want to increase yield, which variable should you adjust? By how much would yield increase if you doubled the catalyst loading (from 2.5% to 5%)?

# Your code here

3b. What are the limitations of using this linear model for process optimization?

Your answer here:

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