Problem Statement
Build a model which predicts sales based on the money spent on different platforms for marketing.
Dataset - https://www.kaggle.com/datasets/ashydv/advertising-dataset
Equation of linear regression
\(y = c + m_1x_1 + m_2x_2 + ... + m_nx_n\)
In our case:
\(y = c + m_1 \times TV\)
The \(m\) values are called the model coefficients or model parameters.
Mainly there are 7 assumptions taken while using Linear Regression:
Please refer : https://www.geeksforgeeks.org/assumptions-of-linear-regression/
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# Dataset Handling
import numpy as np
import pandas as pd
from sklearn.model_selection import train_test_split
# Data Visualisation
import matplotlib.pyplot as plt
import seaborn as sns
#Model Training
from sklearn.linear_model import LinearRegression
#Evaluation
from sklearn.metrics import mean_squared_error, r2_score
from sklearn.feature_selection import f_regression
np.set_printoptions(suppress=True):::
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advertising = pd.DataFrame(pd.read_csv("advertising.csv"))
advertising.head()| TV | Radio | Newspaper | Sales | |
|---|---|---|---|---|
| 0 | 230.1 | 37.8 | 69.2 | 22.1 |
| 1 | 44.5 | 39.3 | 45.1 | 10.4 |
| 2 | 17.2 | 45.9 | 69.3 | 12.0 |
| 3 | 151.5 | 41.3 | 58.5 | 16.5 |
| 4 | 180.8 | 10.8 | 58.4 | 17.9 |
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advertising.shape(200, 4):::
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advertising.info()<class 'pandas.core.frame.DataFrame'>
RangeIndex: 200 entries, 0 to 199
Data columns (total 4 columns):
# Column Non-Null Count Dtype
--- ------ -------------- -----
0 TV 200 non-null float64
1 Radio 200 non-null float64
2 Newspaper 200 non-null float64
3 Sales 200 non-null float64
dtypes: float64(4)
memory usage: 6.4 KB:::
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advertising.describe()| TV | Radio | Newspaper | Sales | |
|---|---|---|---|---|
| count | 200.000000 | 200.000000 | 200.000000 | 200.000000 |
| mean | 147.042500 | 23.264000 | 30.554000 | 15.130500 |
| std | 85.854236 | 14.846809 | 21.778621 | 5.283892 |
| min | 0.700000 | 0.000000 | 0.300000 | 1.600000 |
| 25% | 74.375000 | 9.975000 | 12.750000 | 11.000000 |
| 50% | 149.750000 | 22.900000 | 25.750000 | 16.000000 |
| 75% | 218.825000 | 36.525000 | 45.100000 | 19.050000 |
| max | 296.400000 | 49.600000 | 114.000000 | 27.000000 |
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advertising.isnull().sum()TV 0
Radio 0
Newspaper 0
Sales 0
dtype: int64:::
There are no NULL values in the dataset, hence it is clean.
import matplotlib.pyplot as plt
fig, axes = plt.subplots(nrows=2, ncols=2,figsize=(10,10))
advertising['TV'].plot.box(ax=axes[0,0])
advertising['Radio'].plot.box(ax=axes[0,1])
advertising['Newspaper'].plot.box(ax=axes[1,0])
advertising['Sales'].plot.box(ax=axes[1,1])
plt.show()
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g = pd.plotting.scatter_matrix(advertising, figsize=(10,10))
plt.show()
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advertising.corr()| TV | Radio | Newspaper | Sales | |
|---|---|---|---|---|
| TV | 1.000000 | 0.054809 | 0.056648 | 0.901208 |
| Radio | 0.054809 | 1.000000 | 0.354104 | 0.349631 |
| Newspaper | 0.056648 | 0.354104 | 1.000000 | 0.157960 |
| Sales | 0.901208 | 0.349631 | 0.157960 | 1.000000 |
f = plt.figure(figsize=(5, 5))
plt.matshow(advertising.corr(), fignum=f.number , )
plt.xticks(range(advertising.select_dtypes(['number']).shape[1]), advertising.select_dtypes(['number']).columns, fontsize=14, rotation=45)
plt.yticks(range(advertising.select_dtypes(['number']).shape[1]), advertising.select_dtypes(['number']).columns, fontsize=14)
cb = plt.colorbar()
cb.ax.tick_params(labelsize=14)
plt.title('Correlation Matrix', fontsize=16);
f_stats, p_values = f_regression(advertising[['TV','Radio','Newspaper']].to_numpy(),advertising['Sales'].to_numpy())
f_stats, p_values(array([856.17671282, 27.57467815, 5.0667947 ]),
array([0. , 0.00000039, 0.02548744]))We first assign the feature variable, TV, in this case, to the variable X and the response variable, Sales, to the variable y.
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X = advertising['TV'].to_numpy()
y = advertising['Sales'].to_numpy():::
You now need to split our variable into training and testing sets. You’ll perform this by importing train_test_split from the sklearn.model_selection library. It is usually a good practice to keep 70% of the data in your train dataset and the rest 30% in your test dataset
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X_train, X_test_and_val, y_train, y_test_and_val = train_test_split(X, y, train_size = 0.7,random_state = 100)
X_val, X_test, y_val, y_test = train_test_split(X_test_and_val, y_test_and_val, test_size = 0.5, random_state = 100):::
print(len(X_train),len(X_val),len(X_test))140 30 30model = LinearRegression()X_train.reshape(-1, 1)array([[213.4],
[151.5],
[205. ],
[142.9],
[134.3],
[ 80.2],
[239.8],
[ 88.3],
[ 19.4],
[225.8],
[136.2],
[ 25.1],
[ 38. ],
[172.5],
[109.8],
[240.1],
[232.1],
[ 66.1],
[218.4],
[234.5],
[ 23.8],
[ 67.8],
[296.4],
[141.3],
[175.1],
[220.5],
[ 76.4],
[253.8],
[191.1],
[287.6],
[100.4],
[228. ],
[125.7],
[ 74.7],
[ 57.5],
[262.7],
[262.9],
[237.4],
[227.2],
[199.8],
[228.3],
[290.7],
[276.9],
[199.8],
[239.3],
[ 73.4],
[284.3],
[147.3],
[224. ],
[198.9],
[276.7],
[ 13.2],
[ 11.7],
[280.2],
[ 39.5],
[265.6],
[ 27.5],
[280.7],
[ 78.2],
[163.3],
[213.5],
[293.6],
[ 18.7],
[ 75.5],
[166.8],
[ 44.7],
[109.8],
[ 8.7],
[266.9],
[206.9],
[149.8],
[ 19.6],
[ 36.9],
[199.1],
[265.2],
[165.6],
[140.3],
[230.1],
[ 5.4],
[ 17.9],
[237.4],
[286. ],
[ 93.9],
[292.9],
[ 25. ],
[ 97.5],
[ 26.8],
[281.4],
[ 69.2],
[ 43.1],
[255.4],
[239.9],
[209.6],
[ 7.3],
[240.1],
[102.7],
[243.2],
[137.9],
[ 18.8],
[ 17.2],
[ 76.4],
[139.5],
[261.3],
[ 66.9],
[ 48.3],
[177. ],
[ 28.6],
[180.8],
[222.4],
[193.7],
[ 59.6],
[131.7],
[ 8.4],
[ 13.1],
[ 4.1],
[ 0.7],
[ 76.3],
[250.9],
[273.7],
[ 96.2],
[210.8],
[ 53.5],
[ 90.4],
[104.6],
[283.6],
[ 95.7],
[204.1],
[ 31.5],
[182.6],
[289.7],
[156.6],
[107.4],
[ 43. ],
[248.4],
[116. ],
[110.7],
[187.9],
[139.3],
[ 62.3],
[ 8.6]])::: {.cell _uuid=‘b80a766082e6c9c40c3f09499fec4cfc51f62763’ execution_count=25}
model.fit(X_train.reshape(-1, 1),y_train)LinearRegression()In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
LinearRegression()
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# Print the parameters, i.e. the intercept and the slope of the regression line fitted
b = model.intercept_
w1 = model.coef_[0]
print(str(w1)+"x"+"+"+str(b))0.05454575291590793x+6.948683200001362:::
prediction = model.predict(X_val.reshape(-1, 1))
predictionarray([13.52144643, 18.86693021, 13.1068987 , 17.1923756 , 19.94148154,
10.71234015, 20.13239168, 11.05597839, 9.03233096, 17.60692332,
13.66326538, 18.77420243, 15.11418241, 12.25053038, 18.44147334,
17.72692398, 14.09963141, 11.70507285, 17.99419817, 14.32326899,
9.67597085, 10.6796127 , 13.34144544, 10.79961336, 12.08689312,
16.60328147, 17.48692266, 18.82329361, 17.03419291, 18.75238413])mean_squared_error(y_val.reshape(-1, 1),prediction)4.42099969589266R-Squared (R² or the coefficient of determination) is a statistical measure in a regression model that determines the proportion of variance in the dependent variable that can be explained by the independent variable. In other words, r-squared shows how well the data fit the regression model (the goodness of fit)
r2_score(y_val.reshape(-1, 1),prediction)0.7587703509647371::: {.cell _uuid=‘6e0dc97a88b9fc1d4e975c2fe511e59bd0cd2b8a’ execution_count=31}
plt.scatter(X_train, y_train)
plt.plot(X_train, (w1 * X_train )+ b, 'r')
plt.show()
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predictions = model.predict(X_test.reshape(-1,1)):::
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mean_squared_error(y_test, predictions)3.734113047761241:::
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r_squared = r2_score(y_test, predictions)
r_squared0.8149944458734971:::
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plt.scatter(X_test, y_test)
plt.plot(X_test, (w1 * X_test )+ b, 'r')
plt.show()
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