Statistics Regression & Correlation Analysis 2

Question 1

What is the least squares criterion used for in regression?

Accepted Answer

Minimizing the sum of squared residuals

Answer

Ordinary least squares (OLS) finds the line that minimizes the total of squared vertical distances from the data points.

Question 2

What assumption about residuals is required for ordinary least squares regression to be valid?

Accepted Answer

Residuals are approximately normally distributed with constant variance

Answer

OLS regression assumes residuals are normally distributed, have constant variance (homoscedasticity), and are independent.

Question 3

What does a leverage point in regression mean?

Accepted Answer

An observation with an extreme X value that has potential to strongly influence the regression line

Answer

High-leverage points have unusual predictor values and can disproportionately pull the regression line toward them.

Question 4

Spearman's rank correlation is used instead of Pearson's when?

Accepted Answer

The data are ordinal or the relationship is monotonic but not necessarily linear

Answer

Spearman's correlation uses ranked values and is appropriate for ordinal data or non-linear monotonic relationships.

Question 5

What does heteroscedasticity mean in the context of regression?

Accepted Answer

The variance of residuals changes across levels of the predictor

Answer

Heteroscedasticity means the spread of residuals is not constant, violating the equal-variance assumption of OLS.

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