ISYE 6414 Midterm Summer Study Guide
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Correct | Verified
Assuming that the residuals are normally distributed, the estimated variance of the error terms has the
following sampling distribution under SLR: - ✔✔Chi-square with n-2 degrees of freedom
fitted values def - ✔✔the regression line with parameters replaced with the estimated regression
coefficients
the estimators of the linear regression model are derived by - ✔✔minimizing the sum of squared
differences between observed and expected values of the response variable
the estimators for the regression coefficients are - ✔✔unbiased regardless of the distribution of the data
data
the assumption of normality is needed for - ✔✔the sampling distribution of the estimators of the
regression coefficients and hence for inference
the estimated versus predicted regression line for a given x* have - ✔✔the same expectation
the variability in the prediction comes from - ✔✔the variability due to a new measurement and due to
estimation
residual analysis is used for - ✔✔assessing uncorrelated errors; goodness of fit assessment
we detect departure from the assumption of constant variance - ✔✔when the residuals increase as the
fitted values increase (or decrease, etc)
, There is a direct relationship between the coefficient of determination and the correlation between the
predicting and response variables (T/F) - ✔✔True
The coefficient of determination is interpreted as - ✔✔the percentage of variability in the response
variable explained by the model
Box-Cox transformation is commonly used to improve upon the linearity assumption (T/F) - ✔✔FALSE
If a departure from independence assumption is detected, we transform the response variable to
improve assumption (T/F) - ✔✔FALSE
pooled variance estimator is - ✔✔the variance estimator assuming equal variances
total sum of squares / N-1 = - ✔✔the sample variance estimator assuming equal means and equal
variances
MSE measures - ✔✔the within-treatment variability
if we reject the test of equal means, we conclude - ✔✔that some treatment means are not equal
objective of pairwise comparison - ✔✔to identify the statistically significantly different means
estimated SLP coefficient beta zero measures strength of linear relationship between predicting and
response variables (T/F) - ✔✔FALSE - beta zero is intercept
in SLR, we lose three degrees of freedom when estimating the variance of the error terms (T/F) -
✔✔FALSE - we lose two degrees of freedom because variance estimator only uses estimates for beta
zero and beta one in its calculation
sampling distribution of the estimator of the variance is ____ distributed with ____ degrees of freedom -
✔✔chi-squared, n-2 (under assumption of normality of error terms)
| 2024 Questions & Answers | 100%
Correct | Verified
Assuming that the residuals are normally distributed, the estimated variance of the error terms has the
following sampling distribution under SLR: - ✔✔Chi-square with n-2 degrees of freedom
fitted values def - ✔✔the regression line with parameters replaced with the estimated regression
coefficients
the estimators of the linear regression model are derived by - ✔✔minimizing the sum of squared
differences between observed and expected values of the response variable
the estimators for the regression coefficients are - ✔✔unbiased regardless of the distribution of the data
data
the assumption of normality is needed for - ✔✔the sampling distribution of the estimators of the
regression coefficients and hence for inference
the estimated versus predicted regression line for a given x* have - ✔✔the same expectation
the variability in the prediction comes from - ✔✔the variability due to a new measurement and due to
estimation
residual analysis is used for - ✔✔assessing uncorrelated errors; goodness of fit assessment
we detect departure from the assumption of constant variance - ✔✔when the residuals increase as the
fitted values increase (or decrease, etc)
, There is a direct relationship between the coefficient of determination and the correlation between the
predicting and response variables (T/F) - ✔✔True
The coefficient of determination is interpreted as - ✔✔the percentage of variability in the response
variable explained by the model
Box-Cox transformation is commonly used to improve upon the linearity assumption (T/F) - ✔✔FALSE
If a departure from independence assumption is detected, we transform the response variable to
improve assumption (T/F) - ✔✔FALSE
pooled variance estimator is - ✔✔the variance estimator assuming equal variances
total sum of squares / N-1 = - ✔✔the sample variance estimator assuming equal means and equal
variances
MSE measures - ✔✔the within-treatment variability
if we reject the test of equal means, we conclude - ✔✔that some treatment means are not equal
objective of pairwise comparison - ✔✔to identify the statistically significantly different means
estimated SLP coefficient beta zero measures strength of linear relationship between predicting and
response variables (T/F) - ✔✔FALSE - beta zero is intercept
in SLR, we lose three degrees of freedom when estimating the variance of the error terms (T/F) -
✔✔FALSE - we lose two degrees of freedom because variance estimator only uses estimates for beta
zero and beta one in its calculation
sampling distribution of the estimator of the variance is ____ distributed with ____ degrees of freedom -
✔✔chi-squared, n-2 (under assumption of normality of error terms)
