Two Variable Regression Analysis

What is the purpose of two-variable regression analysis?

• To determine causality between two variables

• To predict the value of one variable based on the value of another variable

• To establish correlation between two variables

• To analyze categorical data

Which statistical measure is used to assess the strength and direction of the relationship between two variables in regression analysis?

• Mean

• Standard deviation

• Coefficient of determination (R-squared)

• Median

In two-variable regression analysis, what does the slope coefficient represent?

• The strength of the relationship between the independent variable and the dependent variable

• The average change in the dependent variable for a one-unit change in the independent variable

• The intercept of the regression line on the y-axis

• The standard error of the regression line

Which of the following is a common assumption in two-variable regression analysis?

• The dependent variable should be normally distributed

• There should be no correlation between the independent variable and the dependent variable

• The sample size should be small

• The relationship between the variables should be nonlinear

How can you assess the significance of the slope coefficient in two-variable regression analysis?

• By calculating the coefficient of determination

• By conducting a t-test on the slope coefficient

• By calculating the p-value for the intercept

• By analyzing the residual plot

What does the term "residual" refer to in two-variable regression analysis?

• The standard deviation of the dependent variable

• The slope coefficient of the regression line

• The correlation coefficient between the independent and dependent variables

• The difference between the predicted values and the actual values of the dependent variable

In two-variable regression analysis, what does a p-value less than the significance level (e.g., 0.05) indicate for the slope coefficient?

• The slope coefficient is statistically significant.

• The slope coefficient is not statistically significant.

• The slope coefficient is equal to zero.

• The slope coefficient is positive.

What is the purpose of residual analysis in two-variable regression analysis?

• To estimate the intercept of the regression line.

• To calculate the coefficient of determination (R-squared).

• To check for violations of regression assumptions.

• To determine the strength of the relationship between the variables.

Which of the following statements is true about outliers in two-variable regression analysis?

• Outliers have no impact on the regression model.

• Outliers always need to be removed from the data.

• Outliers can significantly influence the regression results.

• Outliers only occur in the dependent variable.

What is the purpose of conducting hypothesis testing on the slope coefficient in two-variable regression analysis?

• To assess the normality of the dependent variable.

• To estimate the intercept of the regression line.

• To calculate the standard error of the regression line.

• To determine if there is a significant relationship between the independent and dependent variables.