Econo C2

In a simple linear regression model, what does the equation Y=β₀+β₁X+ϵ represent?

• A quadratic relationship between Y and X

• A linear relationship between Y and X

• The correlation between Y and X

• A model for multiple variables

What does the slope coefficient (β₁​) in a simple linear regression model represent?

• The expected value of Y when X=0

• The strength of the relationship between X and Y

• The rate of change in Y for a one-unit change in X

• The residual variance in the model

In a simple linear regression, what is the purpose of the coefficient of determination (R²)?

• To measure the strength of the linear relationship between Y and X

• To determine the goodness of fit of the model

• To check for multicollinearity

• To calculate the variance of the residuals

Which of the following is an assumption of the simple linear regression model?

• The relationship between the independent and dependent variables is non-linear.

• The residuals are homoscedastic

• The predictor variable X is randomly distributed

• The residuals are normally distributed with a mean of zero.

What does a negative value for the slope coefficient (β₁​) indicate in a simple linear regression?

• A negative slope coefficient indicates an inverse relationship between the independent and dependent variables.
• A negative slope coefficient suggests that the dependent variable increases as the independent variable increases.
• A negative slope coefficient means there is no relationship between the independent and dependent variables.
• A negative slope coefficient indicates a positive relationship between the independent and dependent variables.

What is the purpose of performing hypothesis testing in a simple linear regression model?

• To determine if the slope (β₁​) is significantly different from zero

• To calculate the mean of the dependent variable.
• To predict future outcomes without any data.
• To determine the exact values of the variables.