#1
What does the correlation coefficient measure in linear regression?
The strength and direction of the linear relationship between two variables
The slope of the regression line
The intercept of the regression line
The variance of the dependent variable
#2
Which of the following is a common method for estimating the parameters of a linear regression model?
Least squares estimation
Maximum likelihood estimation
Bayesian estimation
Gradient descent optimization
#3
What is the purpose of the coefficient of correlation in linear regression?
To measure the strength and direction of the linear relationship between two variables
To estimate the intercept of the regression line
To determine the significance level of the independent variable
To compute the sum of squared residuals
#4
Which statement about the residuals in linear regression is true?
They represent the difference between the observed and predicted values of the dependent variable
They are equal to the independent variable
They are used to estimate the coefficient of determination
They determine the significance of the independent variable
#5
What is the formula for the slope (β₁) in simple linear regression?
β₁ = Σ(xy) / Σ(x^2)
β₁ = Σ(x) / Σ(y)
β₁ = Σ(x^2) / Σ(xy)
β₁ = Σ(y) / Σ(x)
#6
Which of the following best describes the purpose of the intercept (β₀) in linear regression?
It represents the predicted value of the dependent variable when the independent variable is zero
It represents the predicted value of the independent variable when the dependent variable is zero
It represents the average of the independent variable
It represents the average of the dependent variable
#7
In linear regression, what does the coefficient of determination (R-squared) indicate?
The proportion of the variance in the dependent variable that is predictable from the independent variable
The sum of squared residuals
The significance level of the independent variable
The slope of the regression line
#8
What does it mean if the p-value associated with a coefficient in linear regression is less than the significance level (e.g., 0.05)?
The coefficient is statistically significant at the given significance level
The coefficient is not statistically significant at the given significance level
The coefficient is equal to zero
The coefficient is negatively correlated
#9
What does multicollinearity refer to in the context of linear regression?
High correlation among independent variables
High correlation between the dependent and independent variables
Low correlation among independent variables
Low correlation between the dependent and independent variables
#10
Which of the following is NOT an assumption of linear regression?
Homoscedasticity
Independence of residuals
Normality of the dependent variable
Linearity
#11
In multiple linear regression, what does the adjusted R-squared measure?
The proportion of the variance in the dependent variable explained by the independent variables
The sum of squared residuals
The significance level of the independent variables
The slope of the regression line
#12
What is the purpose of residual plots in linear regression analysis?
To detect patterns or trends in the residuals
To estimate the coefficients of the regression model
To compute the correlation coefficient
To determine the significance level of the independent variables
#13
Which assumption of linear regression states that the residuals should be normally distributed?
Normality of residuals
Homoscedasticity
Independence of residuals
Linearity
#14
What is the purpose of residual analysis in linear regression?
To assess the validity of the regression assumptions
To estimate the coefficient of determination
To compute the sum of squared residuals
To determine the significance level of the independent variable
#15
Which of the following regression techniques is suitable for modeling nonlinear relationships between variables?
Polynomial regression
Simple linear regression
Multiple linear regression
Logistic regression
#16
What assumption of linear regression states that the variance of the residuals should be constant across all values of the independent variable?
Homoscedasticity
Normality of residuals
Independence of residuals
Linearity
#17
What is the primary goal of transforming variables in regression analysis?
To reduce the influence of outliers.
To make the relationship between variables more linear.
To decrease the variability of the residuals.
To increase the coefficient of determination.