Data Analytics

Gives an idea of the magnitude of errors.

Gives an idea of systematic over- or underprediction.

Compare the root mean squared error and mean absolute error of training and validation data.

y = ßx + E. If x increases by one unit, then y changes by ß units.

log y = ßx + E. If x increases by one unit, then y changes by ß * 100 percent.

y = ß log x + E. If x increases by 100 percent, then y changes by ß units.

log y = ß log x + E. If x increases by 1 percent, then y changes by ß percent.

The RMSE of the training data is lower in the multiple regression compared to the simple one.

When the target variable y is categorical (e.g., color). We only deal with binary outcomes (yes (1), no (0)).

False Positive

False Negative

They can be used for prediction or classification when we have large data sets.

Ridge has a larger bias than the OLS, but a lower variance. This reflects the Bias-Variance Trade-Off.

We minimize the sum of squared residuals to find ßs.

We minimize the sum of squared residuals + a shrinkage penalty with a squared term (power of two) to find ßs.

We minimize the sum of squared residuals + a shrinkage penalty with an absolute value term (power of one) to find ßs.

A combination of RIDGE and LASSO.

Because the constraint of the RIDGE forms a circle, so the ellipse never exactly touches zero.

Ridge: If most variables in the dataset are useful. Lasso: If most variables in the dataset are useless. If uncertain: Use Elastic Net Regression.

Try different tuning parameters, evaluate their performance, and compare. Performance is commonly checked using 10-fold cross-validation.

It involves comparing the mean performances of the tuning parameters on test data blocks.

predicted = ['owner' if p > 0.5 else 'nonowner' for p in owner_df.Probability]

classificationSummary(owner_df.Class, predicted, class_names=['nonowner', 'owner'])

errorrate50 = (1 + 2) / (10 + 2 + 1 + 11)

accuracy50 = 1 - errorrate50 sens50 = 11 / (11 + 1)

spec50 = 10 / (10 + 2)

print(f"Error rate: {errorrate50:4.3f}")

print(f"Accuracy: {accuracy50:4.3f}")

print(f"Sensitivity: {sens50:4.3f}")

print(f"Specificity: {spec50:4.3f}")

summary = pd.DataFrame({"Cutoff": [a, b, c], "Error rate": [a, b, c], "Accuracy": [a, b, c]}) summary

sns.lineplot(data=summary, x="Cutoff", y="Error rate")

ax = summary.plot(x="Cutoff", y="Accuracy", legend=False)

ax2 = ax.twinx() summary.plot(x="Cutoff", y="Error rate",

ax=ax2, legend=True, color="r")

toyota_df = pd.read_csv('ToyotaCorolla.csv', encoding="ISO-8859-1") toyota_df.head()

toyota_df[["Fuel_Type", "Price"]]

toyota_df.Fuel_Type.value_counts() banking_df.Mortgage.value_counts().sort_index()

toyota_df.groupby('Fuel_Type').Price.mean()

sns.boxplot(x="Fuel_Type", y="Price", data=toyota_df, whis=100)

with pd.option_context('mode.use_inf_as_na', True): sns.set(rc={'figure.figsize':(13,5), "figure.dpi":300,})

sns.set_theme(style="whitegrid")sns.swarmplot(x="Fuel_Type", y="Price", data=toyota_df, size=4)

with pd.option_context('mode.use_inf_as_na', True): sns.set(rc={'figure.figsize':(10,8), "figure.dpi":300,})

sns.set_theme(style="whitegrid")sns.stripplot(x="Fuel_Type", y="Price", data=toyota_df)

modg_X = toyota_df[['Fuel_Type']

]modg_X = pd.get_dummies(modg_X, drop_first=True)

modg_X = sm.add_constant(modg_X)

modg_X = modg_X.astype(float) # Make sure that all columns have numerical values# Model estimation and results

modg = sm.OLS(toyota_df['Price'], modg_X)res = modg.fit()print(res.summary())

# Fuel_Type transform in Dummies

X = toyota_df[['Fuel_Type', 'HP']]

y = toyota_df[['Price']]# Transform Fuel_Type in dummies

X = pd.get_dummies(X, drop_first=True)# Split the datatrain_X, valid_X, train_y,

valid_y = train_test_split(X, y, test_size=0.4)# Model

fittingtoyota_ml = LinearRegression()toyota_ml.fit(train_X, train_y)