What does a high R-squared value indicate?
A large proportion of the variance in the dependent variable is explained by the independent variables.
The independent variables are not correlated with the dependent variable.
The model is not a good fit for the data.
The model is a perfect fit for the data.
What distinguishes simple linear regression from multiple linear regression?
Simple linear regression has one independent variable, while multiple linear regression has two or more.
Simple linear regression uses a curved line, while multiple linear regression uses a straight line.
There is no difference; the terms are interchangeable.
Simple linear regression analyzes categorical data, while multiple linear regression analyzes numerical data.
Which of these methods can be used to address heteroscedasticity?
Transforming the dependent variable
Removing outliers
Adding more independent variables
All of the above
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 decrease.
As the independent variable increases, the dependent variable tends to increase.
In forward selection, what criteria is typically used to decide which feature to add at each step?
The feature that results in the smallest increase in R-squared
The feature that results in the largest improvement in model performance
The feature with the highest p-value
The feature that is least correlated with the other features
Which of these is a common visual tool for diagnosing heteroscedasticity?
Box plot
Histogram
Scatter plot of residuals vs. predicted values
Normal probability plot
How does the Mean Squared Error (MSE) penalize larger errors compared to smaller errors?
It squares the errors, giving more weight to larger deviations.
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.
What does a pattern in the residual plot suggest?
The linear model is a good fit for the data.
The residuals are normally distributed.
The linear model is not a good fit for the data, and a non-linear model may be more appropriate.
Which matplotlib function is commonly used to plot the regression line along with the scatter plot of the data?
show()
scatter()
plot()
hist()
Which of the following indicates a strong positive correlation between two variables?
Correlation coefficient (r) close to 0
A p-value greater than 0.05
Correlation coefficient (r) close to -1
Correlation coefficient (r) close to 1