ISYE 6414 FINAL EXAM 2026 ACTUAL QUESTIONS AND
SOLUTIONS RATED A+
✔✔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
✔✔The F-test can be used to evaluate the relationship between two qualitative
variables. - ✔✔False
✔✔The Partial F-Test can test whether a subset of regression coefficients are all equal
to zero. - ✔✔True
✔✔In multiple linear regression, controlling variables are used to control for sample
bias. - ✔✔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. - ✔✔True
✔✔There are four assumptions needed for estimation with multiple linear regression:
mean zero, constant variance, independence, and normality. - ✔✔False (why?)
✔✔Let Y^∗ be the predicted response at x^∗ . The variance of Y^∗ given x^∗ depends
on both the value of x^∗ and the design matrix. - ✔✔True (but the wording was
confusing, so everyone got credit no matter what on this question)
✔✔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). - ✔✔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. - ✔✔True
✔✔For estimating confidence intervals for the regression coefficients, the sampling
distribution used is a normal distribution. - ✔✔False
✔✔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. - ✔✔False
, ✔✔It is possible to produce a model where the overall F-statistic is significant but all the
regression coefficients have insignificant t-statistics. - ✔✔True. (explanation: This can
happen when you have multicollinearity in two or more of the predictors. In that case,
you have an overall model which is significant but on the level of individual predictor,
they might not be since either of the collinear features could be included.)
✔✔Analysis of Variance (ANOVA) is an example of a multiple regression model. -
✔✔True
✔✔For a multiple regression model, both the true errors ϵ and the estimated residuals ϵ-
hat have a constant mean and a constant variance. - ✔✔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. - ✔✔False
✔✔The causation effect of a predicting variable to the response variable can be
captured using multiple linear regression, conditional of other predicting variables in the
model. - ✔✔False
✔✔A high Cook's distance for a particular observation suggests that the observation
could be an influential point. - ✔✔True
✔✔A no-intercept model with one qualitative predicting variable with 3 levels will use 3
dummy variables. - ✔✔True
✔✔If the confidence interval for a regression coefficient contains the value zero, we
interpret that the regression coefficient is definitely equal to zero. - ✔✔False. The
coefficient is plausibly zero, but we cannot be certain that it is
✔✔The larger the coefficient of determination or R-squared, the higher the variability
explained by the simple linear regression model. - ✔✔True. R-squared is the proportion
of variability explained by the model.
✔✔The estimators of the error term variance and of the regression coefficients are
random variables. - ✔✔True. The estimators are 𝛽̂, 𝜎̂^2, and 𝜀̂. These estimators are
functions of the response, which is a random variable. Therefore they are also
random.
✔✔The one-way ANOVA is a linear regression model with one qualitative predicting
variable. - ✔✔True. One-way ANOVA uses one qualitative variable, and it can be
treated as a linear regression model (see Unit 2.2.3).
SOLUTIONS RATED A+
✔✔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
✔✔The F-test can be used to evaluate the relationship between two qualitative
variables. - ✔✔False
✔✔The Partial F-Test can test whether a subset of regression coefficients are all equal
to zero. - ✔✔True
✔✔In multiple linear regression, controlling variables are used to control for sample
bias. - ✔✔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. - ✔✔True
✔✔There are four assumptions needed for estimation with multiple linear regression:
mean zero, constant variance, independence, and normality. - ✔✔False (why?)
✔✔Let Y^∗ be the predicted response at x^∗ . The variance of Y^∗ given x^∗ depends
on both the value of x^∗ and the design matrix. - ✔✔True (but the wording was
confusing, so everyone got credit no matter what on this question)
✔✔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). - ✔✔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. - ✔✔True
✔✔For estimating confidence intervals for the regression coefficients, the sampling
distribution used is a normal distribution. - ✔✔False
✔✔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. - ✔✔False
, ✔✔It is possible to produce a model where the overall F-statistic is significant but all the
regression coefficients have insignificant t-statistics. - ✔✔True. (explanation: This can
happen when you have multicollinearity in two or more of the predictors. In that case,
you have an overall model which is significant but on the level of individual predictor,
they might not be since either of the collinear features could be included.)
✔✔Analysis of Variance (ANOVA) is an example of a multiple regression model. -
✔✔True
✔✔For a multiple regression model, both the true errors ϵ and the estimated residuals ϵ-
hat have a constant mean and a constant variance. - ✔✔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. - ✔✔False
✔✔The causation effect of a predicting variable to the response variable can be
captured using multiple linear regression, conditional of other predicting variables in the
model. - ✔✔False
✔✔A high Cook's distance for a particular observation suggests that the observation
could be an influential point. - ✔✔True
✔✔A no-intercept model with one qualitative predicting variable with 3 levels will use 3
dummy variables. - ✔✔True
✔✔If the confidence interval for a regression coefficient contains the value zero, we
interpret that the regression coefficient is definitely equal to zero. - ✔✔False. The
coefficient is plausibly zero, but we cannot be certain that it is
✔✔The larger the coefficient of determination or R-squared, the higher the variability
explained by the simple linear regression model. - ✔✔True. R-squared is the proportion
of variability explained by the model.
✔✔The estimators of the error term variance and of the regression coefficients are
random variables. - ✔✔True. The estimators are 𝛽̂, 𝜎̂^2, and 𝜀̂. These estimators are
functions of the response, which is a random variable. Therefore they are also
random.
✔✔The one-way ANOVA is a linear regression model with one qualitative predicting
variable. - ✔✔True. One-way ANOVA uses one qualitative variable, and it can be
treated as a linear regression model (see Unit 2.2.3).
