ISYE 6414 UPDATED 2026 EXAM SCRIPT QUESTIONS AND SOLUTIONS RATED

ISYE 6414 UPDATED 2026 EXAM SCRIPT QUESTIONS AND
SOLUTIONS RATED A+
✔✔In ANOVA, we assume the variance of the response variable is different for each
population. - ✔✔False (Explanation: is the same across all populations)

✔✔The F-test in ANOVA compares the between variability versus the within variability. -
✔✔True

✔✔In testing for subsets of coefficients in a multiple linear regression, the null
hypothesis we test
for is that all coefficients are equal;
H_0: B_1 = B_2 = ... = B_kf - ✔✔False (Explanation: The null hypothesis is that all
coefficients are equal to zero; none are significant in predicting the response.)

✔✔The only assumptions for a simple linear regression model are linearity, constant
variance, and normality. - ✔✔False

✔✔In a simple linear regression model, the variable of interest is the response variable.
- ✔✔True

✔✔The constant variance assumption is diagnosed by plotting the predicting variable
vs. the response variable. - ✔✔False

✔✔β 1 is an unbiased estimator for β 0 . - ✔✔False

✔✔The estimator σ ^ 2 is a fixed variable. - ✔✔False

✔✔The ANOVA model with a qualitative predicting variable with k levels/classes will
have k + 1 parameters to estimate. - ✔✔True

✔✔Under the normality assumption, the estimator for β 1 is a linear combination of
normally distributed random variables. - ✔✔True

✔✔A negative value of β 1 is consistent with an inverse relationship between x and y . -
✔✔True

✔✔In the simple linear regression model, we lose three degrees of freedom because of
the estimation of the three model parameters β 0 , β 1 , σ 2 . - ✔✔False

✔✔The regression coefficient is used to measure the linear dependence between two
variables. - ✔✔False

, ✔✔If the constant variance assumption in ANOVA does not hold, the inference on the
equality of the means will not be reliable. - ✔✔True

✔✔If one confidence interval in the pairwise comparison does not include zero, we
conclude that the two means are plausibly equal. - ✔✔False

✔✔The mean sum of square errors in ANOVA measures variability within groups. -
✔✔True

✔✔Only the log-transformation of the response variable should be used when the
normality assumption does not hold. - ✔✔False

✔✔If one confidence interval in the pairwise comparison includes only positive values,
we conclude that the difference in means is positive, and statistically significant. -
✔✔True

✔✔The number of degrees of freedom of the χ 2 (chi-square) distribution for the pooled
variance estimator is N − k + 1 where k is the number of samples. - ✔✔False

✔✔For assessing the normality assumption of the ANOVA model, we can use the
quantile-quantile normal plot and the historgram of the residuals. - ✔✔True

✔✔One-way ANOVA is a linear regression model with more than one qualitative
predicting variables. - ✔✔False

✔✔The sampling distribution for the variance estimator in ANOVA is χ 2 (chi-square)
with N - k degrees of freedom. - ✔✔False

✔✔In simple linear regression, we can diagnose the assumption of constant-variance
by plotting the residuals against fitted values. - ✔✔True

✔✔If response variable Y has a quadratic relationship with a predictor variable X, it is
possible to model the relationship using multiple linear regression. - ✔✔True

✔✔The R^2 value represents the percentage of variability in the response that can be
explained by the linear regression on the predictors. Models with higher R^2 are always
preferred over models with lower R^2 . - ✔✔False

✔✔For the model y = β 0 + β 1 x 1 + ... + β p x p + ϵ , where ϵ ∼ N ( 0 , σ^2 ) , there are
p+1 parameters to be estimated - ✔✔False