What does a residual represent in linear regression?
The slope of the regression line.
The difference between the actual and predicted values of the dependent variable.
The predicted value of the dependent variable.
The intercept of the regression line.
If a Durbin-Watson test statistic is close to 2, what does it suggest about the residuals?
They are homoscedastic
They exhibit a linear pattern
They are normally distributed
They are independent
Which of the following indicates a strong positive correlation between two variables?
Correlation coefficient (r) close to 1
Correlation coefficient (r) close to -1
Correlation coefficient (r) close to 0
A p-value greater than 0.05
What is the method used in linear regression to estimate the model parameters that minimize the sum of squared errors?
Method of Moments
Maximum Likelihood Estimation
Bayesian Estimation
Least Squares Estimation
What graphical tool is commonly used to visualize the relationship between two continuous variables in linear regression?
Histogram
Bar chart
Pie chart
Scatter plot
Backward elimination in linear regression involves removing features based on what criterion?
The feature with the lowest p-value
The feature that contributes the least to multicollinearity
The feature that results in the smallest decrease in model performance
The feature with the highest correlation with the target variable
What type of visualization tool is commonly used to initially assess the relationship between two continuous variables in linear regression?
Why is normality of errors an important assumption in linear regression?
It guarantees the homoscedasticity of the errors
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
Which of the following is the general equation for a simple linear regression model?
y = e^(b0 + b1*x)
y = b0 * x^b1
y = b0 + b1x1 + b2x2 + ... + bn*xn
y = b0 + b1*x + e
What is the main difference between forward selection and backward elimination in linear 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 is used for classification, while backward elimination is used for regression.
Forward selection starts with no features and adds one by one, while backward elimination starts with all features and removes one by one.
There is no difference; both techniques achieve the same outcome.