#install required library
!pip install statsmodels==0.14.0
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#import required libraries
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import *
import seaborn as sns
import statsmodels.api as sm
from statsmodels.formula.api import ols
from tabulate import tabulate
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# Load the data from file
df = pd.read_csv('2012FuelEcon.csv')
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# 1. Use descriptive statistics to summarize the data
# a. Summary for each variable in the data set
summary = df.describe(include='all')
print(summary)
skewness_value1 = skew(df['Displacement'])
kurtosis_value1 = kurtosis(df['Displacement'])
skewness_value2 = skew(df['Hwy MPG'])
kurtosis_value2 = kurtosis(df['Hwy MPG'])
print(f'Skewness of Displacement: {skewness_value1}')
print(f'Kurtosis of Displacement: {kurtosis_value1}')
print(f'Skewness of Hwy MPG: {skewness_value2}')
print(f'Kurtosis of Hwy MPG: {kurtosis_value2}')
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# b. A bar chart or pie chart showing the number of cars and trucks attributable to the Manufacturer
# Set a color palette for the plot
sns.set_palette("pastel")
# Create a bar plot with customizations
plt.figure(figsize=(12, 8))
df["Manufacturer"].value_counts().plot(kind="bar", edgecolor='black', width=0.8)
plt.xlabel("Manufacturer", fontsize=14)
plt.ylabel("Number of Cars and Trucks", fontsize=14)
plt.title("Number of Cars and Trucks by Manufacturer", fontsize=16)
plt.xticks(rotation=45, ha="right", fontsize=12) # Rotate x-axis labels for better readability
# Add value labels on top of each bar
for i, value in enumerate(df["Manufacturer"].value_counts()):
plt.text(i, value + 2, str(value), ha='center', va='bottom', fontsize=10)
# Remove y-axis ticks
plt.tick_params(axis='y', which='both', left=False)
plt.show()
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# c. A crosstabulation of type of drive versus Displacement
cross_tab = pd.crosstab(df['Displacement'],df['Drive'], margins=True, margins_name='Total')
print(cross_tab)
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# d. A scatter diagram to explore the relationship between Displacement and Hwy MPG
# Set a seaborn style for better aesthetics
sns.set(style="whitegrid")
# Scatter plot with regression line
plt.figure(figsize=(12, 8))
sns.regplot(x="Displacement", y="Hwy MPG", data=df, scatter_kws={'s':50}, line_kws={'color': 'red'})
plt.xlabel("Displacement (liters)", fontsize=14)
plt.ylabel("Highway MPG (miles per gallon)", fontsize=14)
plt.title("Scatter Plot of Displacement and Highway MPG", fontsize=16)
# grid lines
plt.grid(True, linestyle='--', alpha=0.7)
plt.show()
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# e. A crosstabulation showing the number of cars and trucks attributable to the type of drive versus type of fuel
print(pd.crosstab(df["Drive"], df["Fuel"]))
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# f. A histogram to explore the frequency of the fuel efficiency rating for highway driving
plt.figure(figsize=(10, 6))
plt.hist(df['Hwy MPG'], bins=20, color='skyblue', edgecolor='black', alpha=0.7)
plt.title('Histogram of Highway MPG', fontsize=16)
plt.xlabel("Highway MPG (miles per gallon)", fontsize=14)
plt.ylabel('Frequency', fontsize=14)
# Grid lines
plt.grid(axis='y', linestyle='--', alpha=0.7)
plt.show()
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mean_displacement = df.groupby('Fuel')['Displacement'].mean().reset_index()
# Plotting the bar chart
plt.figure(figsize=(8, 5))
ax=sns.barplot(x='Displacement', y='Fuel', data=mean_displacement, palette='viridis', edgecolor='black')
for index, value in enumerate(mean_displacement['Displacement']):
ax.text(value + 0.01, index, f'{value:.2f}', ha='left', va='center', fontsize=10)
plt.title('Mean Engine Displacement by Fuel Type')
plt.xlabel('Mean Engine Displacement (Liters)')
plt.ylabel('Fuel Type')
plt.show()
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Assuming equal variance:
reg = df[df["Fuel"] == "Regular"]["Displacement"]
pre = df[df["Fuel"] == "Premium"]["Displacement"]
t_stat_eq, p_value_eq = ttest_ind(pre, reg, equal_var=True,alternative='two-sided')
print("The t-statistic is", t_stat_eq)
print("The p-value is", p_value_eq)
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Assuming unequal variance:
reg = df[df["Fuel"] == "Regular"]["Displacement"]
pre = df[df["Fuel"] == "Premium"]["Displacement"]
t_stat_ueq, p_value_ueq = ttest_ind(pre, reg, equal_var=False,alternative='two-sided')
print("The t-statistic is", t_stat_ueq)
print("The p-value is", p_value_ueq)
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b. Any difference between the variability of fuel efficiency rating for highway driving of BMW and Kia companies
Inferences for two variance
# Separate data for BMW and Kia
bmw_data = df[df['Manufacturer'] == 'BMW']
kia_data = df[df['Manufacturer'] == 'Kia']
# Create a box plot
plt.figure(figsize=(8, 6))
sns.boxplot(x='Manufacturer', y='Hwy MPG', data=pd.concat([bmw_data, kia_data]))
plt.xlabel('Manufacturer')
plt.ylabel('Highway MPG')
plt.title('Variability of Fuel Efficiency Rating (Highway MPG)\nBMW vs. Kia')
plt.show()
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n1=len(bmw_data)
n2=len(kia_data)
bmw = df[df["Manufacturer"] == "BMW"]["Hwy MPG"]
kia = df[df["Manufacturer"] == "Kia"]["Hwy MPG"]
variance_bmw = bmw.var()
variance_kia = kia.var()
print("n1 = ",n1)
print("n2 = ",n2)
print("s1^2 = ",variance_bmw)
print("s2^2 = ",variance_kia)
F_stat= variance_bmw/variance_kia
print("F_statistic = ",F_stat)
p_value = 2 * (1 - f.cdf(F_stat, n1 - 1, n2 - 1))
print("P_value = ",p_value)
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mean = df["Displacement"].mean()
std = df["Displacement"].std()
n = len(df)
a=0.05
z = norm.ppf(1-a/2)
lower = mean - z * std / np.sqrt(n)
upper = mean + z * std / np.sqrt(n)
print(n)
print("Mean of sample of engine's displacement = ",mean)
print("Variance of sample of engine's displacement = ",std**2)
print("The 95% confidence interval estimate of the mean engine's displacement is", (lower, upper))
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# Assuming df is your DataFrame
mean_displacement = df['Displacement'].mean()
std_displacement = df['Displacement'].std()
n = len(df)
# Calculate standard error of the mean
sem = std_displacement / np.sqrt(n)
# Calculate margin of error for 95% confidence interval
margin_of_error = t.ppf(0.975, df=n-1) * sem
# Calculate the confidence interval
confidence_interval = (mean_displacement - margin_of_error, mean_displacement + margin_of_error)
# Plotting the bar chart with error bars
plt.figure(figsize=(8, 6))
sns.barplot(x=['Mean Engine Displacement'], y=[mean_displacement], color='skyblue')
plt.errorbar(x=['Mean Engine Displacement'], y=[mean_displacement], yerr=[margin_of_error], fmt='none', ecolor='black', capsize=10)
plt.title('95% Confidence Interval for Mean Engine Displacement')
plt.ylabel('Engine Displacement (Liters)')
plt.show()
# Print the confidence interval
print(f'95% Confidence Interval: {confidence_interval}')
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Question 4: Use analysis of variance to test for:
a. Any significant differences in the engine’s displacement due to the type of drive. Use a 0.05 level of significance.
f_statistic, p_value_drive = f_oneway(
df[df["Drive"] == "F"]["Displacement"],
df[df["Drive"] == "A"]["Displacement"],
df[df["Drive"] == "R"]["Displacement"]
)
print("a. ANOVA for differences in engine displacement due to the type of drive:")
print("F-statistic:", f_statistic)
print("p-value:", p_value_drive)
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b. Any significant differences in the engine’s displacement due to the manufacturer, the type of drive, and interaction. Use a 0.05 level of significance.
# b. ANOVA for differences in engine displacement due to the manufacturer, drive, and interaction
model = ols("Displacement ~ Manufacturer + Drive + Manufacturer:Drive", data=df).fit()
table = sm.stats.anova_lm(model)
print("\nb. ANOVA for differences in engine displacement due to the manufacturer, drive, and interaction:")
print(table)
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from scipy.stats import chi2_contingency
obs = pd.crosstab(df["Manufacturer"], df["Drive"])
chi2, p_value, dof, exp = chi2_contingency(obs)
print("The chi-square statistic is", chi2)
print("The p-value is", p_value)
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from scipy.stats import jarque_bera
w, p_value = jarque_bera(df["Hwy MPG"])
print("The Jacques-Bera statistic is", w)
print("The p-value is", p_value)
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from scipy.stats import chi2
# Significance level
alpha = 0.05
# Degrees of freedom
df_chi2 = 2
# Calculate critical value for chi-square distribution
critical_value = chi2.ppf(1 - alpha, df_chi2)
print(f"Critical value at {alpha} significance level with {df_chi2} degrees of freedom: {critical_value}")
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# 7. Develop an estimated regression equation that can be used to predict the fuel efficiency for highway driving given the engine’s displacement. Test for significance using 0.05 level of significance
from sklearn.linear_model import LinearRegression
from sklearn.metrics import r2_score
from scipy.stats import t
X = df[["Displacement"]]
y = df["Hwy MPG"]
# Fit the linear regression model
reg = LinearRegression().fit(X, y)
print("The estimated regression equation is Hwy MPG = {:.2f} - {:.4f} * Displacement".format(reg.intercept_, reg.coef_[0]))
# Calculate the coefficient of determination (R-squared)
print("The coefficient of determination is", r2_score(y, reg.predict(X)))
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# Calculate the standard error of the residuals
residuals = y - reg.predict(X)
se = np.sqrt(np.sum(residuals**2) / (len(df) - 2))
# Calculate the standard error of the coefficients (b0,b1)
se_b0 = se * np.sqrt(1/len(df) + np.mean(X.values)**2 / np.sum((X.values - np.mean(X.values))**2))
se_b1 = se / np.sqrt(np.sum((X.values - np.mean(X.values))**2))
# Calculate the t-statistics and p-values
t_b0 = reg.intercept_ / se_b0
t_b1 = reg.coef_[0] / se_b1
p_b0 = 2 * (1 - t.cdf(abs(t_b0), len(df) - 2))
p_b1 = 2 * (1 - t.cdf(abs(t_b1), len(df) - 2))
# Results
print("The t-statistic and p-value for the intercept are", t_b0, "and", p_b0)
print("The t-statistic and p-value for the coefficient are", t_b1, "and", p_b1)
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help(pd.read_csv)
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df.columns
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df.set_index('Drive')
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df.columns
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