What is the main difference between forward selection and backward elimination in linear regression?
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.
There is no difference; both techniques achieve the same outcome.
Forward selection starts with no features and adds one by one, while backward elimination starts with all features and removes one by one.
If the coefficient of determination (R-squared) for a linear regression model is 0.8, what does this indicate?
80% of the variation in the dependent variable is explained by the independent variable.
20% of the variation in the dependent variable is explained by the independent variable.
The model is a poor fit for the data.
There is a weak relationship between the independent and dependent variables.
Who is credited as a pioneer in developing the method of least squares, a foundational element of linear regression?
Blaise Pascal
Ada Lovelace
Carl Friedrich Gauss
Alan Turing
What is the method used in linear regression to estimate the model parameters that minimize the sum of squared errors?
Bayesian Estimation
Maximum Likelihood Estimation
Least Squares Estimation
Method of Moments
What type of visualization tool is commonly used to initially assess the relationship between two continuous variables in linear regression?
Pie chart
Bar chart
Scatter plot
Histogram
What is the purpose of splitting the dataset into training and testing sets in Linear Regression?
To visualize the relationship between variables.
To evaluate the model's performance on unseen data.
To reduce the dimensionality of the data.
To handle missing values in the dataset.
Can the R-squared value be negative?
No, it always ranges between 0 and 1.
Yes, if the model fits the data worse than a horizontal line.
No, it is always positive.
Yes, if there is a perfect negative correlation between the variables.
Which matplotlib function is commonly used to plot the regression line along with the scatter plot of the data?
plot()
show()
scatter()
hist()
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.
How does the Mean Squared Error (MSE) penalize larger errors compared to smaller errors?
It takes the absolute value of the errors, ignoring the sign.
It doesn't; all errors are penalized equally.
It squares the errors, giving more weight to larger deviations.
It uses a logarithmic scale to compress larger errors.