ISYE 6414 MIDTERM 2 PART 1
EXAMINATION TEST COMPLETE SOLVED
QUESTIONS
◉ How to calculate standardized residuals in R
Answer: Use rstandard(lm.full) for standardized residuals. Use
rstudent(lm.full) for studentized (jackknife) residuals.
◉ What is the SLR model equation
Answer: Y_i = beta_0 + beta_1 x_i + epsilon_i, epsilon_i ~ N(0,
sigma^2).
◉ What are the parameters in SLR
Answer: beta_0 (intercept), beta_1 (slope), sigma^2 (error
variance). Total 3 parameters.
◉ What is the difference between response and predictor
variables
Answer: Response variable is random and varies with predictor.
Predictor variable is fixed and set before response is measured.
◉ What is the objective of SLR
Answer: To fit a non-deterministic linear model that minimizes
residuals using least squares criterion.
, ◉ What does R-squared measure
Answer: R^2 = 1 - SSE/SST. Measures proportion of total
variability in response explained by the model. In SLR, R^2 = r^2.
◉ What is the difference between R^2 and adjusted R^2
Answer: R^2 never decreases when adding predictors. Adjusted
R^2 penalizes extra predictors and is used for model comparison.
◉ What are the ANOVA assumptions
Answer: Constant variance (homogeneity), Independence,
Normality. Linearity is NOT required for ANOVA.
◉ What is the ANOVA null hypothesis
Answer: H0: mu_1 = mu_2 = ... = mu_k (all group means are equal).
◉ What is the ANOVA alternative hypothesis
Answer: At least one pair of group means are statistically
significantly different.
◉ What is Tukey HSD used for
Answer: To perform pairwise comparisons of group means after
ANOVA while controlling family-wise error rate.
◉ What is goodness-of-fit
EXAMINATION TEST COMPLETE SOLVED
QUESTIONS
◉ How to calculate standardized residuals in R
Answer: Use rstandard(lm.full) for standardized residuals. Use
rstudent(lm.full) for studentized (jackknife) residuals.
◉ What is the SLR model equation
Answer: Y_i = beta_0 + beta_1 x_i + epsilon_i, epsilon_i ~ N(0,
sigma^2).
◉ What are the parameters in SLR
Answer: beta_0 (intercept), beta_1 (slope), sigma^2 (error
variance). Total 3 parameters.
◉ What is the difference between response and predictor
variables
Answer: Response variable is random and varies with predictor.
Predictor variable is fixed and set before response is measured.
◉ What is the objective of SLR
Answer: To fit a non-deterministic linear model that minimizes
residuals using least squares criterion.
, ◉ What does R-squared measure
Answer: R^2 = 1 - SSE/SST. Measures proportion of total
variability in response explained by the model. In SLR, R^2 = r^2.
◉ What is the difference between R^2 and adjusted R^2
Answer: R^2 never decreases when adding predictors. Adjusted
R^2 penalizes extra predictors and is used for model comparison.
◉ What are the ANOVA assumptions
Answer: Constant variance (homogeneity), Independence,
Normality. Linearity is NOT required for ANOVA.
◉ What is the ANOVA null hypothesis
Answer: H0: mu_1 = mu_2 = ... = mu_k (all group means are equal).
◉ What is the ANOVA alternative hypothesis
Answer: At least one pair of group means are statistically
significantly different.
◉ What is Tukey HSD used for
Answer: To perform pairwise comparisons of group means after
ANOVA while controlling family-wise error rate.
◉ What is goodness-of-fit
