What type of visualization tool is commonly used to initially assess the relationship between two continuous variables in linear regression?
Bar chart
Histogram
Scatter plot
Pie chart
Feature selection in linear regression primarily aims to:
Make the model more complex and harder to interpret
Increase the number of features used for prediction
Improve model performance and generalization by focusing on the most relevant predictors
Ensure that all features have a statistically significant p-value
What does the 'fit_intercept' parameter in 'LinearRegression()' control?
Whether to calculate the slope of the line.
Whether to normalize the data before fitting.
Whether to calculate the intercept (bias) of the line.
Whether to use gradient descent for optimization.
Which of the following is the general equation for a simple linear regression model?
y = b0 * x^b1
y = e^(b0 + b1*x)
y = b0 + b1*x + e
y = b0 + b1x1 + b2x2 + ... + bn*xn
What does a pattern in the residual plot suggest?
The residuals are normally distributed.
There is no relationship between the independent and dependent variables.
The linear model is a good fit for the data.
The linear model is not a good fit for the data, and a non-linear model may be more appropriate.
What function from scikit-learn is used to perform Linear Regression?
linear_model.LinearRegression()
linear_model.LogisticRegression()
model_selection.train_test_split()
preprocessing.StandardScaler()
What does the assumption of independence in linear regression refer to?
Independence between the observations
Independence between the independent and dependent variables
Independence between the coefficients of the regression model
Independence between the errors and the dependent variable
What is the primary goal of feature selection in linear regression?
Improve the model's interpretability and reduce overfitting
Increase the complexity of the model
Maximize the number of features used in the model
Introduce bias into the model
What does a correlation coefficient of 0 indicate?
No linear relationship
A strong positive linear relationship
A strong negative linear relationship
A perfect linear relationship
What does the linearity assumption in linear regression imply?
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 data points are evenly distributed around the regression line.
The dependent variable must have a normal distribution.