ISYE 6414 MIDTERM EXAM STUDY GUIDE QUESTIONS WITH
COMPLETE SOLUTIONS
We can assess the constant variance assumption in linear regression by plotting the
l, l, l, l, l, l, l, l, l, l, l, l,
l, residuals vs. fitted values. -- Answer ✔✔ True
l, l, l, l, l, l, l,
If one confidence interval in the pairwise comparison in ANOVA includes zero, we
l, l, l, l, l, l, l, l, l, l, l, l,
l, conclude that the two corresponding means are plausibly equal. -- Answer ✔✔ True
l, l, l, l, l, l, l, l, l, l, l, l,
The assumption of normality is not required in linear regression to make inference on the
l, l, l, l, l, l, l, l, l, l, l, l, l, l,
l, regression coefficients. -- Answer ✔✔ False (Explanation: is required)
l, l, l, l, l, l, l, l,
We cannot estimate a multiple linear regression model if the predicting variables are linearly
l, l, l, l, l, l, l, l, l, l, l, l, l,
l, independent. -- Answer ✔✔ False (Explanation: linearly dependent) l, l, l, l, l, l, l,
If a predicting variable is a categorical variable with 5 categories in a linear regression model
l, l, l, l, l, l, l, l, l, l, l, l, l, l, l,
l, without intercept, we will include 5 dummy variables. -- Answer ✔✔ True
l, l, l, l, l, l, l, l, l, l, l,
If the normality assumption does not hold for a regression, we may use a transformation on
l, l, l, l, l, l, l, l, l, l, l, l, l, l, l,
l, the response variable. -- Answer ✔✔ True
l, l, l, l, l, l,
The prediction of the response variable has higher uncertainty than the estimation of the
l, l, l, l, l, l, l, l, l, l, l, l, l,
l, mean response. -- Answer ✔✔ True
l, l, l, l, l,
Statistical inference for linear regression under normality relies on large sample size. --
l, l, l, l, l, l, l, l, l, l, l, l,
l, Answer ✔✔ False (Explanation: small sample size is fine)
l, l, l, l, l, l, l, l,
, A nonlinear relationship between the response variable and a predicting variable cannot be
l, l, l, l, l, l, l, l, l, l, l, l,
l, modeled using regression. -- Answer ✔✔ False (Explanation: Nonlinear relationships can
l, l, l, l, l, l, l, l, l, l,
l, often be modeled using linear regression by including polynomial terms of the predicting
l, l, l, l, l, l, l, l, l, l, l, l,
l, variable, for example.) l, l,
Assumption of normality in linear regression is required for confidence intervals, prediction
l, l, l, l, l, l, l, l, l, l, l,
l, intervals, and hypothesis testing. -- Answer ✔✔ True l, l, l, l, l, l, l,
If the confidence interval for a regression coefficient contains the value zero, we interpret
l, l, l, l, l, l, l, l, l, l, l, l, l,
l, that the regression coefficient is plausibly equal to zero. -- Answer ✔✔ True
l, l, l, l, l, l, l, l, l, l, l, l,
The smaller the coefficient of determination or R-squared, the higher the variability
l, l, l, l, l, l, l, l, l, l, l,
l, explained bythe simple linear regression. -- Answer ✔✔ False (Explanation: The larger the
l, l, l, l, l, l, l, l, l, l, l, l,
l, R-squared)
The estimators of the variance parameter and of the regression coefficients in a regression
l, l, l, l, l, l, l, l, l, l, l, l, l,
l, model are random variables. -- Answer ✔✔ True
l, l, l, l, l, l, l,
The standard error in linear regression indicates how far the data points are from the
l, l, l, l, l, l, l, l, l, l, l, l, l, l,
l, regression line, on average. -- Answer ✔✔ True l, l, l, l, l, l, l,
A linear regression model is a good fit to the data set if the R-squared is above 0.90. --
l, l, l, l, l, l, l, l, l, l, l, l, l, l, l, l, l, l,
l, Answer ✔✔ False (Explanation: There are other things to check: assumptions, MSE, etc.)
l, l, l, l, l, l, l, l, l, l, l, l,
In ANOVA, we assume the variance of the response variable is different for each
l, l, l, l, l, l, l, l, l, l, l, l, l,
l, population. -- Answer ✔✔ False (Explanation: is the same across all populations)
l, l, l, l, l, l, l, l, l, l, l,
The F-test in ANOVA compares the between variability versus the within variability. --
l, l, l, l, l, l, l, l, l, l, l, l,
l, Answer ✔✔ True l, l,
COMPLETE SOLUTIONS
We can assess the constant variance assumption in linear regression by plotting the
l, l, l, l, l, l, l, l, l, l, l, l,
l, residuals vs. fitted values. -- Answer ✔✔ True
l, l, l, l, l, l, l,
If one confidence interval in the pairwise comparison in ANOVA includes zero, we
l, l, l, l, l, l, l, l, l, l, l, l,
l, conclude that the two corresponding means are plausibly equal. -- Answer ✔✔ True
l, l, l, l, l, l, l, l, l, l, l, l,
The assumption of normality is not required in linear regression to make inference on the
l, l, l, l, l, l, l, l, l, l, l, l, l, l,
l, regression coefficients. -- Answer ✔✔ False (Explanation: is required)
l, l, l, l, l, l, l, l,
We cannot estimate a multiple linear regression model if the predicting variables are linearly
l, l, l, l, l, l, l, l, l, l, l, l, l,
l, independent. -- Answer ✔✔ False (Explanation: linearly dependent) l, l, l, l, l, l, l,
If a predicting variable is a categorical variable with 5 categories in a linear regression model
l, l, l, l, l, l, l, l, l, l, l, l, l, l, l,
l, without intercept, we will include 5 dummy variables. -- Answer ✔✔ True
l, l, l, l, l, l, l, l, l, l, l,
If the normality assumption does not hold for a regression, we may use a transformation on
l, l, l, l, l, l, l, l, l, l, l, l, l, l, l,
l, the response variable. -- Answer ✔✔ True
l, l, l, l, l, l,
The prediction of the response variable has higher uncertainty than the estimation of the
l, l, l, l, l, l, l, l, l, l, l, l, l,
l, mean response. -- Answer ✔✔ True
l, l, l, l, l,
Statistical inference for linear regression under normality relies on large sample size. --
l, l, l, l, l, l, l, l, l, l, l, l,
l, Answer ✔✔ False (Explanation: small sample size is fine)
l, l, l, l, l, l, l, l,
, A nonlinear relationship between the response variable and a predicting variable cannot be
l, l, l, l, l, l, l, l, l, l, l, l,
l, modeled using regression. -- Answer ✔✔ False (Explanation: Nonlinear relationships can
l, l, l, l, l, l, l, l, l, l,
l, often be modeled using linear regression by including polynomial terms of the predicting
l, l, l, l, l, l, l, l, l, l, l, l,
l, variable, for example.) l, l,
Assumption of normality in linear regression is required for confidence intervals, prediction
l, l, l, l, l, l, l, l, l, l, l,
l, intervals, and hypothesis testing. -- Answer ✔✔ True l, l, l, l, l, l, l,
If the confidence interval for a regression coefficient contains the value zero, we interpret
l, l, l, l, l, l, l, l, l, l, l, l, l,
l, that the regression coefficient is plausibly equal to zero. -- Answer ✔✔ True
l, l, l, l, l, l, l, l, l, l, l, l,
The smaller the coefficient of determination or R-squared, the higher the variability
l, l, l, l, l, l, l, l, l, l, l,
l, explained bythe simple linear regression. -- Answer ✔✔ False (Explanation: The larger the
l, l, l, l, l, l, l, l, l, l, l, l,
l, R-squared)
The estimators of the variance parameter and of the regression coefficients in a regression
l, l, l, l, l, l, l, l, l, l, l, l, l,
l, model are random variables. -- Answer ✔✔ True
l, l, l, l, l, l, l,
The standard error in linear regression indicates how far the data points are from the
l, l, l, l, l, l, l, l, l, l, l, l, l, l,
l, regression line, on average. -- Answer ✔✔ True l, l, l, l, l, l, l,
A linear regression model is a good fit to the data set if the R-squared is above 0.90. --
l, l, l, l, l, l, l, l, l, l, l, l, l, l, l, l, l, l,
l, Answer ✔✔ False (Explanation: There are other things to check: assumptions, MSE, etc.)
l, l, l, l, l, l, l, l, l, l, l, l,
In ANOVA, we assume the variance of the response variable is different for each
l, l, l, l, l, l, l, l, l, l, l, l, l,
l, population. -- Answer ✔✔ False (Explanation: is the same across all populations)
l, l, l, l, l, l, l, l, l, l, l,
The F-test in ANOVA compares the between variability versus the within variability. --
l, l, l, l, l, l, l, l, l, l, l, l,
l, Answer ✔✔ True l, l,
