9.6 Checking Conditions for Inference in Regression

• What is one of the important conditions for inference in regression?

  Random sampling
• A random sample enables us to infer the regression relationship found in the sample applies to the population
• To check for linearity, one can visually inspect a scatterplot
• If residuals are correlated, it can lead to inaccurate hypothesis tests.


  True
• To check for linearity, a scatterplot should show points forming a curved pattern.

  False
• Linearity is an important condition for inference in regression
• If the scatterplot shows a curved pattern, the linearity condition is violated.


  True
• To check for independence, we can plot the residuals against their order
• Normally distributed residuals ensure accurate confidence intervals and hypothesis tests.


  True
• Equal variance in regression is also known as homoscedasticity.
• Equal variance ensures that the standard errors of regression coefficients are reliable.

  True
• Random sampling ensures that the sample is representative
• What does linearity mean in the context of regression inference?

  Linear relationship between x and y
• What does independence mean in the context of regression inference?

  Residuals are independent
• What is one advantage of random sampling in regression inference?

  Ensures population representation
• What should be done if the relationship between variables is non-linear?

  Cannot use regression inference
• A linear relationship implies that as x increases, y changes at a constant rate.


  True
• Independence in regression means that the residuals should be independent of each other.
• The Durbin-Watson test is used to formally assess the independence of residuals.


  True
• A histogram is used to visualize the distribution of residuals.
• To check for equal variance, residuals are plotted against predicted values.


  True
• A residual plot with a funnel shape indicates a violation of equal variance.
• A random sample makes the data more representative of the population.


  True
• A linear relationship implies that as x increases, y increases (or decreases) at a constant rate.


  True
• Independence ensures that one data point does not influence the error of another
• Random sampling can be difficult to implement effectively
• Match the relationship type with its characteristic:

  Linear ↔️ Points form a straight line

  Non-Linear ↔️ Points form a curved pattern
• To check for linearity, we can visually inspect a scatterplot
• Correlated residuals can lead to inflated confidence intervals.


  True
• The normality condition in regression requires that the residuals follow a normal distribution.
• A normal probability plot checks if the residuals align with a theoretical normal distribution.


  True
• The Breusch-Pagan test is a statistical test for equal variance.