Sales prediction

Version without data splitting.

Setup

import numpy as np
import pandas as pd
import altair as alt

from sklearn.linear_model import LinearRegression
from sklearn.metrics import r2_score
from sklearn.metrics import mean_squared_error
from sklearn.metrics import mean_absolute_error

Data

Import data

df = pd.read_csv('https://raw.githubusercontent.com/kirenz/datasets/master/advertising.csv')

Data structure

df

	Market	TV	radio	newspaper	sales
0	1	230.1	37.8	69.2	22.1
1	2	44.5	39.3	45.1	10.4
2	3	17.2	45.9	69.3	9.3
3	4	151.5	41.3	58.5	18.5
4	5	180.8	10.8	58.4	12.9
...	...	...	...	...	...
195	196	38.2	3.7	13.8	7.6
196	197	94.2	4.9	8.1	9.7
197	198	177.0	9.3	6.4	12.8
198	199	283.6	42.0	66.2	25.5
199	200	232.1	8.6	8.7	13.4

200 rows × 5 columns

df.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 200 entries, 0 to 199
Data columns (total 5 columns):
 #   Column     Non-Null Count  Dtype  
---  ------     --------------  -----  
 0   Market     200 non-null    int64  
 1   TV         200 non-null    float64
 2   radio      200 non-null    float64
 3   newspaper  200 non-null    float64
 4   sales      200 non-null    float64
dtypes: float64(4), int64(1)
memory usage: 7.9 KB

Data corrections

# variable Market is categorical
df['Market'] = df['Market'].astype('category')

Variable lists

# define outcome variable as y_label
y_label = 'sales'

# select features
features = df.drop(columns=[y_label, 'Market']).columns.tolist()

# create feature data
X = df[features]

# create response
y = df[y_label]

Analysis

Descriptive statistics

df.describe().T

	count	mean	std	min	25%	50%	75%	max
TV	200.0	147.0425	85.854236	0.7	74.375	149.75	218.825	296.4
radio	200.0	23.2640	14.846809	0.0	9.975	22.90	36.525	49.6
newspaper	200.0	30.5540	21.778621	0.3	12.750	25.75	45.100	114.0
sales	200.0	14.0225	5.217457	1.6	10.375	12.90	17.400	27.0

Exploratory data analysis

alt.Chart(df).mark_bar().encode(
    alt.X(alt.repeat("column"), type="quantitative", bin=True),
    y='count()',
).properties(
    width=150,
    height=150
).repeat(
    column=['sales', 'TV', 'radio', 'newspaper']
)

alt.Chart(df).mark_circle().encode(
    alt.X(alt.repeat("column"), type='quantitative'),
    alt.Y(alt.repeat("row"), type='quantitative')
).properties(
    width=150,
    height=150
).repeat(
    row=['sales', 'TV', 'radio', 'newspaper'],
    column=['sales', 'TV', 'radio', 'newspaper']
).interactive()

Correlations

# inspect correlation between outcome and possible predictors
corr = df.corr()
corr[y_label].sort_values(ascending=False)

sales        1.000000
TV           0.782224
radio        0.576223
newspaper    0.228299
Name: sales, dtype: float64

# take a look at all correlations
corr.style.background_gradient(cmap='Blues')

	TV	radio	newspaper	sales
TV	1.000000	0.054809	0.056648	0.782224
radio	0.054809	1.000000	0.354104	0.576223
newspaper	0.056648	0.354104	1.000000	0.228299
sales	0.782224	0.576223	0.228299	1.000000

Model

Select model

# select the linear regression model
reg = LinearRegression()

Fit model

# Fit the model to the data
reg.fit(X, y)

LinearRegression()

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Coefficients

# intercept
intercept = pd.DataFrame({
    "Name": ["Intercept"],
    "Coefficient":[reg.intercept_]}
    )

	Name	Coefficient
0	Intercept	2.939
1	TV	0.046
2	radio	0.189
3	newspaper	-0.001

# make a slope table
slope = pd.DataFrame({
    "Name": features,
    "Coefficient": reg.coef_}
)

# combine estimates of intercept and slopes
table = pd.concat([intercept, slope], ignore_index=True, sort=False)

round(table, 3)

Evaluation

# obtain predictions
y_pred = reg.predict(X)

# R squared
r2_score(y, y_pred).round(3)

0.897

# MSE
mean_squared_error(y, y_pred).round(3)

2.784

# RMSE
mean_squared_error(y, y_pred, squared=False).round(3)

1.669

# MAE
mean_absolute_error(y, y_pred).round(3)

1.252