What graphical tool is commonly used to visualize the relationship between two continuous variables in linear regression?
Scatter plot
Histogram
Pie chart
Bar chart
Why is a residual plot useful in evaluating a linear regression model?
To calculate the R-squared value.
To predict future values of the dependent variable.
To determine the slope of the regression line.
To check for non-linearity and other violations of the linear regression assumptions.
In forward selection, what criteria is typically used to decide which feature to add at each step?
The feature that results in the largest improvement in model performance
The feature that results in the smallest increase in R-squared
The feature that is least correlated with the other features
The feature with the highest p-value
Which Python library is primarily used for numerical computing and provides support for arrays and matrices, essential for Linear Regression calculations?
NumPy
matplotlib
scikit-learn
pandas
A positive coefficient of the independent variable in a simple linear regression model indicates what?
The independent variable has no impact on the dependent variable.
There is no relationship between the independent and dependent variables.
As the independent variable increases, the dependent variable tends to increase.
As the independent variable increases, the dependent variable tends to decrease.
Which of the following is NOT an assumption of linear regression?
Normality of residuals
Multicollinearity
Homoscedasticity
Linearity
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 does a correlation coefficient of 0 indicate?
No linear relationship
A strong positive linear relationship
A strong negative linear relationship
A perfect linear relationship
What is the primary goal of feature selection in linear regression?
Increase the complexity of the model
Introduce bias into the model
Improve the model's interpretability and reduce overfitting
Maximize the number of features used in the model
Which matplotlib function is commonly used to plot the regression line along with the scatter plot of the data?
plot()
show()
hist()
scatter()