Module 3B Regression Analysis Flashcards
What does the simple linear regression equation describe?
It describes how the dependent variable 𝑦 is related to the independent variable 𝑥 and an error term. The error term accounts for variability in 𝑦 not explained by 𝑥.
What does the Least Squares Method minimize in regression analysis?
It minimizes the sum of squared errors (SSE), where each residual (error) is the difference between the actual and the predicted observation of the dependent variable.
What is the experimental region in regression analysis?
It is the range of values of the independent variables used to estimate the model, beyond which predictions are considered risky (extrapolation).
What are the components of the Total Sum of Squares (SST)?
SST = SSR (sum of squares due to regression) + SSE (sum of squares due to error). SSR measures the deviation of predicted values from the sample mean, while SSE measures the squared deviations of predicted from observed values.
What does the Coefficient of Determination (R²) indicate in regression analysis?
R² indicates the proportion of the variability in the dependent variable that is explained by the regression model. It is the square of the correlation between predicted and observed values, and it ranges from 0 to 1.
What does each coefficient in a multiple regression model represent?
Each coefficient represents the change in the mean value of the dependent variable 𝑦 for a one-unit increase in an independent variable, holding all other variables constant.
What distribution should the values of 𝑦 at a given 𝑥 adhere to in regression analysis?
The values should follow a normal distribution around the linear trend, and the distribution of residuals should be random.
What is multicollinearity and how is it handled in regression analysis?
Multicollinearity occurs when two or more independent variables are highly correlated. For inference, one of the variables may be removed; for prediction, both can be kept.
What are interaction effects in regression analysis?
Interaction effects occur when the relationship between a dependent variable and an independent variable varies at different levels of another independent variable, demonstrating moderation.
What are the two types of interval estimates used in regression prediction?
Confidence intervals estimate the mean value of 𝑦 given the independent variables, while prediction intervals estimate individual 𝑦 values given the independent variables.
