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 does a residual represent in linear regression?
The difference between the actual and predicted values of the dependent variable.
The slope of the regression line.
The predicted value of the dependent variable.
The intercept of the regression line.
A positive coefficient of the independent variable in a simple linear regression model indicates what?
As the independent variable increases, the dependent variable tends to decrease.
As the independent variable increases, the dependent variable tends to increase.
The independent variable has no impact on the dependent variable.
There is no relationship between the independent and dependent variables.
Why is a residual plot useful in evaluating a linear regression model?
To determine the slope of the regression line.
To check for non-linearity and other violations of the linear regression assumptions.
To predict future values of the dependent variable.
To calculate the R-squared value.
If a Durbin-Watson test statistic is close to 2, what does it suggest about the residuals?
They are homoscedastic
They are normally distributed
They are independent
They exhibit a linear pattern
What does a correlation coefficient of 0 indicate?
A perfect linear relationship
A strong negative linear relationship
No linear relationship
A strong positive linear relationship
What does a pattern in the residual plot suggest?
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.
The linear model is a good fit for the data.
What is the purpose of splitting the dataset into training and testing sets in Linear Regression?
To reduce the dimensionality of the data.
To visualize the relationship between variables.
To evaluate the model's performance on unseen data.
To handle missing values in the dataset.
What does a high R-squared value indicate?
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.
A large proportion of the variance in the dependent variable is explained by the independent variables.
Which of the following is NOT a benefit of feature selection in linear regression?
Improved model interpretability
Reduced computational cost
Increased risk of overfitting
Potential for better generalization to new data