Which of the following situations might make feature selection particularly important?
When computational resources are unlimited
Having a small dataset with a very large number of features
When all features are highly correlated with the target variable
Having a very large dataset with only a few features
What is the method used in linear regression to estimate the model parameters that minimize the sum of squared errors?
Maximum Likelihood Estimation
Least Squares Estimation
Bayesian Estimation
Method of Moments
Which Python library is primarily used for numerical computing and provides support for arrays and matrices, essential for Linear Regression calculations?
scikit-learn
pandas
NumPy
matplotlib
What is the primary goal of feature selection in linear regression?
Maximize the number of features used in the model
Improve the model's interpretability and reduce overfitting
Introduce bias into the model
Increase the complexity of the model
What does a residual represent in linear regression?
The intercept of the regression line.
The slope of the regression line.
The predicted value of the dependent variable.
The difference between the actual and predicted values of the dependent variable.
Which of these is a common visual tool for diagnosing heteroscedasticity?
Normal probability plot
Histogram
Scatter plot of residuals vs. predicted values
Box plot
Why is normality of errors an important assumption in linear regression?
It is necessary for the calculation of the regression coefficients
It validates the use of hypothesis testing for the model's coefficients
It ensures the linearity of the relationship between variables
It guarantees the homoscedasticity of the errors
Which of the following is NOT a benefit of feature selection in linear regression?
Reduced computational cost
Increased risk of overfitting
Potential for better generalization to new data
Improved model interpretability
What does a pattern in the residual plot suggest?
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.
The linear model is not a good fit for the data, and a non-linear model may be more appropriate.
What does a high R-squared value indicate?
The independent variables are not correlated with the dependent variable.
The model is a perfect fit for the data.
The model is not a good fit for the data.
A large proportion of the variance in the dependent variable is explained by the independent variables.