What is the purpose of splitting the dataset into training and testing sets in Linear Regression?
To evaluate the model's performance on unseen data.
To visualize the relationship between variables.
To handle missing values in the dataset.
To reduce the dimensionality of the data.
In the context of linear regression, what is an error term?
The variation in the independent variable.
The difference between the observed value of the dependent variable and the predicted value.
The difference between the slope and the intercept of the regression line.
A mistake made in collecting or entering data.
In forward selection, what criteria is typically used to decide which feature to add at each step?
The feature that is least correlated with the other features
The feature that results in the largest improvement in model performance
The feature with the highest p-value
The feature that results in the smallest increase in R-squared
What is the primary goal of feature selection in linear regression?
Introduce bias into the model
Improve the model's interpretability and reduce overfitting
Increase the complexity of the model
Maximize the number of features used in the model
Backward elimination in linear regression involves removing features based on what criterion?
The feature that results in the smallest decrease in model performance
The feature with the highest correlation with the target variable
The feature with the lowest p-value
The feature that contributes the least to multicollinearity
What is the main difference between forward selection and backward elimination in linear regression?
There is no difference; both techniques achieve the same outcome.
Forward selection is used for classification, while backward elimination is used for regression.
Forward selection starts with all features and removes one by one, while backward elimination starts with no features and adds one by one.
Forward selection starts with no features and adds one by one, while backward elimination starts with all features and removes one by one.
What function from scikit-learn is used to perform Linear Regression?
model_selection.train_test_split()
preprocessing.StandardScaler()
linear_model.LogisticRegression()
linear_model.LinearRegression()
How does the Mean Squared Error (MSE) penalize larger errors compared to smaller errors?
It doesn't; all errors are penalized equally.
It takes the absolute value of the errors, ignoring the sign.
It uses a logarithmic scale to compress larger errors.
It squares the errors, giving more weight to larger deviations.
What does a pattern in the residual plot suggest?
The linear model is not a good fit for the data, and a non-linear model may be more appropriate.
The residuals are normally distributed.
The linear model is a good fit for the data.
There is no relationship between the independent and dependent variables.
Which of these is a common visual tool for diagnosing heteroscedasticity?
Scatter plot of residuals vs. predicted values
Box plot
Histogram
Normal probability plot