In [1]:
# Code attribution: Yiyin Shen, Tyler Caraza-Harter
# Imports
import sklearn
import sklearn.linear_model
import numpy
import pandas
import statsmodels.api
import matplotlib.pyplot as plt
In [2]:
# Read the data and plot the regression coefficients
data = pandas.read_csv("NewGrades.csv")
features = ["Exam1", "Project", "Lecture", "Quiz", "Lab"]
x = data[features]
y = data["Exam2"]
reg = sklearn.linear_model.LinearRegression()
reg.fit(x, y)
plt.bar(features, reg.coef_)
Out[2]:
<BarContainer object of 5 artists>
In [3]:
# Compute the score R^2 and adj R^2 of the regression
r2 = reg.score(x, y)
[r2, 1 - (1 - r2) * (len(y) - 1) / (len(y) - 5 - 1)]
Out[3]:
[0.42000633317727665, 0.4119508655825166]
In [4]:
# Manually compute the score using the formula
y_pred = reg.predict(x)
y_bar = numpy.mean(y)
(sum((y_pred - y_bar) ** 2)) / (sum((y - y_bar) ** 2))
Out[4]:
0.42000633317727676
In [5]:
# Remove one column and run the regression and compare the scores
scores = []
for col in x:
xi = x.drop(col, axis = 1)
reg.fit(xi, y)
scores.append(reg.score(xi, y))
plt.bar(features, scores)
Out[5]:
<BarContainer object of 5 artists>
In [6]:
# Use statsmodel for the comparison (not required for P6)
model = statsmodels.api.OLS(y, statsmodels.api.add_constant(x)).fit()
print(model.summary())
OLS Regression Results
==============================================================================
Dep. Variable: Exam2 R-squared: 0.420
Model: OLS Adj. R-squared: 0.412
Method: Least Squares F-statistic: 52.14
Date: Tue, 21 Nov 2023 Prob (F-statistic): 1.32e-40
Time: 22:08:41 Log-Likelihood: -847.96
No. Observations: 366 AIC: 1708.
Df Residuals: 360 BIC: 1731.
Df Model: 5
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
const -4.6815 2.833 -1.653 0.099 -10.252 0.889
Exam1 0.3986 0.038 10.371 0.000 0.323 0.474
Project -0.1215 0.258 -0.471 0.638 -0.629 0.386
Lecture 0.5225 0.156 3.357 0.001 0.216 0.829
Quiz 1.4005 0.262 5.340 0.000 0.885 1.916
Lab -0.5823 0.995 -0.586 0.559 -2.538 1.373
==============================================================================
Omnibus: 10.077 Durbin-Watson: 0.861
Prob(Omnibus): 0.006 Jarque-Bera (JB): 10.103
Skew: -0.387 Prob(JB): 0.00640
Kurtosis: 3.253 Cond. No. 455.
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.