What graphical tool is commonly used to visualize the relationship between two continuous variables in linear regression?
Scatter plot
Histogram
Bar chart
Pie chart
Can the R-squared value be negative?
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.
No, it always ranges between 0 and 1.
What does a pattern in the residual plot suggest?
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.
The linear model is a good fit for the data.
There is no relationship between the independent and dependent variables.
What does a correlation coefficient of 0 indicate?
A strong negative linear relationship
No linear relationship
A perfect linear relationship
A strong positive linear relationship
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.
What type of visualization tool is commonly used to initially assess the relationship between two continuous variables in linear regression?
Who is credited as a pioneer in developing the method of least squares, a foundational element of linear regression?
Ada Lovelace
Blaise Pascal
Carl Friedrich Gauss
Alan Turing
Who is credited with developing the foundational principles of linear regression?
Albert Einstein
Isaac Newton
Sir Francis Galton
Marie Curie
Which of these methods can be used to address heteroscedasticity?
Adding more independent variables
Transforming the dependent variable
All of the above
Removing outliers
What does the 'fit_intercept' parameter in 'LinearRegression()' control?
Whether to normalize the data before fitting.
Whether to calculate the intercept (bias) of the line.
Whether to use gradient descent for optimization.
Whether to calculate the slope of the line.