Who is credited with developing the foundational principles of linear regression?
Sir Francis Galton
Marie Curie
Albert Einstein
Isaac Newton
What does a high R-squared value indicate?
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.
The model is a perfect fit for the data.
The independent variables are not correlated with the dependent variable.
Why is normality of errors an important assumption in linear regression?
It ensures the linearity of the relationship between variables
It is necessary for the calculation of the regression coefficients
It validates the use of hypothesis testing for the model's coefficients
It guarantees the homoscedasticity of the errors
How does the Mean Squared Error (MSE) penalize larger errors compared to smaller errors?
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.
It takes the absolute value of the errors, ignoring the sign.
What is the ideal shape of a residual plot for a well-fitted linear regression model?
A U-shape.
A straight line.
An inverted U-shape.
Random scatter with no discernible pattern.
What does a pattern in the residual plot suggest?
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.
The residuals are normally distributed.
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
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
Method of Moments
Least Squares Estimation
What type of visualization tool is commonly used to initially assess the relationship between two continuous variables in linear regression?
Bar chart
Pie chart
Scatter plot
Histogram
What does the linearity assumption in linear regression imply?
The data points are evenly distributed around the regression line.
The independent variables are unrelated to each other.
The relationship between the dependent and independent variables can be best represented by a straight line.
The dependent variable must have a normal distribution.