Regression residuals — normality?
Residuals should be normally distributed for inference.
Homoskedasticity — assumption?
Residual variance should be constant across X.
Random residual pattern — indicator?
No systematic pattern in residuals vs X.
Slope estimate — formula?
Sum of cross-products divided by sum of X deviations.
Intercept estimate — formula?
Mean of Y minus slope times mean of X.
Slope significance test — statistic?
t = (b̂1−0)/SE(b̂1).
Prediction interval — key component?
Includes forecast ± t·standard error of forecast.
Dummy variable — coefficient interpretation?
Difference in means between groups.
Correlation test — used when?
Variables are approximately normal and continuous.
Spearman correlation — basis?
Ranks of data, for non-normal distributions.
Chi-square — degrees of freedom?
(rows−1)×(columns−1).
Variance test — statistic?
Chi-square = (n−1)s²/σ₀².
Choosing test — when paired?
Dependent samples, same subjects measured twice.
Significance level — effect?
Lower α reduces Type I error, increases Type II error.
Standard error — formula?
σ/√n if σ known; estimated from data otherwise.
CLT — role?
Allows normal approximation for large samples.
Answer 16 questions on Fundamentals of Regression and Hypothesis Testing.
1. Which statement best describes the normality assumption in simple linear regression?
2. What does a non-random pattern in a residuals-versus-X plot most strongly suggest?
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