Flashcard: Fundamentals of Regression and Hypothesis Testing — 16 carte

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.