What does the assumption of independence in linear regression refer to?
Independence between the errors and the dependent variable
Independence between the coefficients of the regression model
Independence between the independent and dependent variables
Independence between the observations
What is the purpose of the coefficient of determination (R-squared) in linear regression?
To assess the linearity assumption of the model.
To measure the proportion of variation in the dependent variable explained by the independent variable(s).
To determine the statistical significance of the model.
To identify the presence of outliers in the data.
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 the 'fit_intercept' parameter in 'LinearRegression()' control?
Whether to use gradient descent for optimization.
Whether to calculate the intercept (bias) of the line.
Whether to calculate the slope of the line.
Whether to normalize the data before fitting.
In the context of linear regression, what is an error term?
The variation in the independent variable.
A mistake made in collecting or entering data.
The difference between the slope and the intercept of the regression line.
The difference between the observed value of the dependent variable and the predicted value.
What does the linearity assumption in linear regression imply?
The data points are evenly distributed around the regression line.
The dependent variable must have a normal distribution.
The independent variables are unrelated to each other.
The relationship between the dependent and independent variables can be best represented by a straight line.
Which of the following is the general equation for a simple linear regression model?
y = b0 + b1*x + e
y = e^(b0 + b1*x)
y = b0 * x^b1
y = b0 + b1x1 + b2x2 + ... + bn*xn
Which of the following is NOT an assumption of linear regression?
Homoscedasticity
Normality of residuals
Linearity
Multicollinearity
How does the Mean Squared Error (MSE) penalize larger errors compared to smaller errors?
It uses a logarithmic scale to compress larger errors.
It takes the absolute value of the errors, ignoring the sign.
It squares the errors, giving more weight to larger deviations.
It doesn't; all errors are penalized equally.
Which matplotlib function is commonly used to plot the regression line along with the scatter plot of the data?
plot()
show()
hist()
scatter()