ISYE 6414 Midterm Prep | 2024 Questions & Answers |
100% Correct | Verified
We can assess the constant variance assumption in linear regression by plotting the residuals vs. fitted
values. - ✔✔True
If one confidence interval in the pairwise comparison in ANOVA includes zero, we conclude that the two
corresponding means are plausibly equal. - ✔✔True
The assumption of normality is not required in linear regression to make inference on the regression
coefficients. - ✔✔False (Explanation: is required)
We cannot estimate a multiple linear regression model if the predicting variables are linearly
independent. - ✔✔False (Explanation: linearly dependent)
If a predicting variable is a categorical variable with 5 categories in a linear regression model without
intercept, we will include 5 dummy variables. - ✔✔True
If the normality assumption does not hold for a regression, we may use a transformation on the
response variable. - ✔✔True
The prediction of the response variable has higher uncertainty than the estimation of the mean
response. - ✔✔True
Statistical inference for linear regression under normality relies on large sample size. - ✔✔False
(Explanation: small sample size is fine)
A nonlinear relationship between the response variable and a predicting variable cannot be modeled
using regression. - ✔✔False (Explanation: Nonlinear relationships can often be modeled using linear
regression by including polynomial terms of the predicting variable, for example.)
, Assumption of normality in linear regression is required for confidence intervals, prediction intervals,
and hypothesis testing. - ✔✔True
If the confidence interval for a regression coefficient contains the value zero, we interpret that the
regression coefficient is plausibly equal to zero. - ✔✔True
The smaller the coefficient of determination or R-squared, the higher the variability explained bythe
simple linear regression. - ✔✔False (Explanation: The larger the R-squared)
The estimators of the variance parameter and of the regression coefficients in a regression model are
random variables. - ✔✔True
The standard error in linear regression indicates how far the data points are from the regression line, on
average. - ✔✔True
A linear regression model is a good fit to the data set if the R-squared is above 0.90. - ✔✔False
(Explanation: There are other things to check: assumptions, MSE, etc.)
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
100% Correct | Verified
We can assess the constant variance assumption in linear regression by plotting the residuals vs. fitted
values. - ✔✔True
If one confidence interval in the pairwise comparison in ANOVA includes zero, we conclude that the two
corresponding means are plausibly equal. - ✔✔True
The assumption of normality is not required in linear regression to make inference on the regression
coefficients. - ✔✔False (Explanation: is required)
We cannot estimate a multiple linear regression model if the predicting variables are linearly
independent. - ✔✔False (Explanation: linearly dependent)
If a predicting variable is a categorical variable with 5 categories in a linear regression model without
intercept, we will include 5 dummy variables. - ✔✔True
If the normality assumption does not hold for a regression, we may use a transformation on the
response variable. - ✔✔True
The prediction of the response variable has higher uncertainty than the estimation of the mean
response. - ✔✔True
Statistical inference for linear regression under normality relies on large sample size. - ✔✔False
(Explanation: small sample size is fine)
A nonlinear relationship between the response variable and a predicting variable cannot be modeled
using regression. - ✔✔False (Explanation: Nonlinear relationships can often be modeled using linear
regression by including polynomial terms of the predicting variable, for example.)
, Assumption of normality in linear regression is required for confidence intervals, prediction intervals,
and hypothesis testing. - ✔✔True
If the confidence interval for a regression coefficient contains the value zero, we interpret that the
regression coefficient is plausibly equal to zero. - ✔✔True
The smaller the coefficient of determination or R-squared, the higher the variability explained bythe
simple linear regression. - ✔✔False (Explanation: The larger the R-squared)
The estimators of the variance parameter and of the regression coefficients in a regression model are
random variables. - ✔✔True
The standard error in linear regression indicates how far the data points are from the regression line, on
average. - ✔✔True
A linear regression model is a good fit to the data set if the R-squared is above 0.90. - ✔✔False
(Explanation: There are other things to check: assumptions, MSE, etc.)
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
