ISYE 6414 Regression Analysis 2026 Summer Midterm Practice EXAM LATEST VERSION QUESTIONS AND ANSWERS.pdf

ISYE 6414 Regression Analysis 2026 Summer Midterm
Practice EXAM LATEST VERSION 2026-2027 QUESTIONS
AND ANSWERS

The sampling distribution of the estimated regression coefficients is Centered at the true
regression parameters. - answer>>True


The sampling distribution of the estimated regression coefficients is the t-distribution assuming
that the variance of the error term is unknown an replaced by its estimate. - answer>>True


The estimators for the regression coefficients are Uunbiased regardless of the distribution of the
data. correct - answer>>True


Multiple linear regression is a general model encompassing both ANOVA and simple linear
regression. correct - answer>>True


The regression coefficients can be estimated only if the predicting variables are not linearly
dependent. - answer>>True


1. The means of the k populations
2. The sample means of the k populations
3. The sample means of the k samples
are NOT all the model parameters in ANOVA - answer>>True


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


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

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


LaTeX: \beta_1 β 1 is an unbiased estimator for LaTeX: \beta_0 β 0 . - answer>>False


The estimator LaTeX: \hat \sigma^2 σ ^ 2 is a fixed variable. - answer>>False


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


Under the normality assumption, the estimator for LaTeX: \beta_1 β 1 is a linear combination of
normally distributed random variables. - answer>>True


A negative value of LaTeX: \beta_1 β 1 is consistent with an inverse relationship between LaTeX:
x x and LaTeX: y y . - answer>>True


In the simple linear regression model, we lose three degrees of freedom because of the
estimation of the three model parameters LaTeX: \beta_0,\:\beta_1,\sigma^2 β 0 , β 1 , σ 2 . -
answer>>False


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


Only the log-transformation of the response variable should be used when the normality
assumption does not hold. - answer>>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. - answer>>True


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

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


The sampling distribution for the variance estimator in ANOVA is LaTeX: \chi^2 χ 2 (chi-square)
with N - k degrees of freedom. - answer>>False


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


The LaTeX: R^2 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 LaTeX: R^2 R 2 are
always preferred over models with lower LaTeX: R^2 R 2 . - answer>>True


For the model LaTeX: y=\beta_0+\beta_1x_1+...+\beta_px_p+\epsilon y = β 0 + β 1 x 1 + ... + β p
x p + ϵ , where LaTeX: \epsilon\sim N(0,\sigma^2) ϵ ∼ N ( 0 , σ 2 ) , there are p+1 parameters to
be estimated - answer>>False


The F-test can be used to evaluate the relationship between two qualitative variables. -
answer>>False


The Partial F-Test can test whether a subset of regression coefficients are all equal to zero. -
answer>>True


In multiple linear regression, controlling variables are used to control for sample bias. -
answer>>True


In a multiple regression model with 7 predicting variables, the sampling distribution of the
estimated variance of the error terms is a chi-squared distribution with n-8 degrees of freedom.
- answer>>True

, There are four assumptions needed for estimation with multiple linear regression: mean zero,
constant variance, independence, and normality. - answer>>False


Let LaTeX: Y^* Y ∗ be the predicted response at LaTeX: x^* x ∗ . The variance of LaTeX: Y^* Y ∗
given LaTeX: x^* x ∗ depends on both the value of LaTeX: x^* x ∗ and the design matrix. -
answer>>True


Suppose x1 was not found to be significant in the model specified with lm(y ~ x1 + x2 + x3). Then
x1 will also not be significant in the model lm(y ~ x1 + x2). - answer>>False


When estimating confidence values for the mean response for all instances of the predicting
variables, we should use a critical point based on the F-distribution to correct for the
simultaneous inference. - answer>>True


In a multiple linear regression model with quantitative predictors, the coefficient corresponding
to one predictor is interpreted as the estimated expected change in the response variable when
there is a one unit change in that predictor. - answer>>False


It is possible to produce a model where the overall F-statistic is significant but all the regression
coefficients have insignificant t-statistics. - answer>>True


Analysis of Variance (ANOVA) is an example of a multiple regression model. - answer>>True


For a multiple regression model, both the true errors LaTeX: \epsilon ϵ and the estimated
residuals LaTeX: \hat \epsilon ϵ ^ have a constant mean and a constant variance. -
answer>>False


If the p-value of the overall F-test is close to 0, we can conclude all the predicting variable
coefficients are significantly nonzero. - answer>>False