ISYE 6414 Regression Modules 1-2 || with 100% Error-free
Solutions.
Assuming that the data are normally distributed, under the simple linear model, the estimated
variance has the following sampling distribution: correct answers Chi-squared with n-2 degrees
of freedom.
The fitted values are defined as? correct answers The regression line with parameters replaced
with the estimated regression coefficients.
The estimators fo the linear regression model are derived by? correct answers Minimizing the
sum of squared differences between the observed and expected values of the response variable.
The estimators for the regression coefficients are: correct answers Unbiased regardless of the
distribution of the data.
The assumption of normality: correct answers 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* correct answers have the same
expectation.
The variability in the prediction comes from correct answers the variability due to a new
measurement and due to estimation.
Residual analysis can only be used to assess uncorrelated errors. correct answers False
Independence assumption can be assess using the normal probability plot. correct answers False
Independence assumption can be assessed using the residuals vs fitted values. correct answers
False
We detect departure from the assumption of constant variance correct answers when the
residuals vs fitted values are larger in the ends but smaller in the middle.
If a departure from normality is detected, we transform the predicting variable to improve upon
the normality assumption. correct answers False
If a departure from the independence assumption is detected, we transform the response variable
to improve upon the independence assumption. correct answers False
The Box-Cox transformation is commonly used to improve upon the linearity assumption.
correct answers False
, In evaluating a simple linear model correct answers there is a direct relationship between the
coefficient of determination and the correlation between the predicting and response variables.
Goodness of fit assessment is done by correct answers residual analysis
R-squared (the coefficient of variation) is interpreted as correct answers the percentage of
variability in the response variable explained by the model.
The parameters of ANOVA are correct answers the k sample means and the population variance.
The pooled variance estimator is correct answers the sample variance estimator assuming equal
variances.
In ANOVA, the mean sum of squares divided by N-1 is correct answers the sample variance
estimator assuming equal means and equal variances.
MSE measures correct answers the within-treatment variability.
MSSTr measures correct answers the between treatment variability.
If we reject the test of equal means, we conclude that at least one pair of means are different.
correct answers True
If we do not reject the test of equal means, we conclude that means are definitely all equal.
correct answers False
If we reject the test of equal means, we conclude that all treatment means are not equal. correct
answers False
In ANOVA, the objective of residual analysis is to correct answers evaluate departures from the
model assumptions.
In ANOVA, the objective of the pairwise comparison is correct answers To identify the
statistically significant different means
For assessing the normality assumption of the ANOVA model, we can only use the quantile-
quantile normal plot of the residuals. correct answers False
The constant variance assumption is diagnosed using the histogram? correct answers False
The estimator sigma^2 is a random variable? correct answers True
The regression coefficients are used to measure the linear dependence between two variables?
correct answers False
Solutions.
Assuming that the data are normally distributed, under the simple linear model, the estimated
variance has the following sampling distribution: correct answers Chi-squared with n-2 degrees
of freedom.
The fitted values are defined as? correct answers The regression line with parameters replaced
with the estimated regression coefficients.
The estimators fo the linear regression model are derived by? correct answers Minimizing the
sum of squared differences between the observed and expected values of the response variable.
The estimators for the regression coefficients are: correct answers Unbiased regardless of the
distribution of the data.
The assumption of normality: correct answers 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* correct answers have the same
expectation.
The variability in the prediction comes from correct answers the variability due to a new
measurement and due to estimation.
Residual analysis can only be used to assess uncorrelated errors. correct answers False
Independence assumption can be assess using the normal probability plot. correct answers False
Independence assumption can be assessed using the residuals vs fitted values. correct answers
False
We detect departure from the assumption of constant variance correct answers when the
residuals vs fitted values are larger in the ends but smaller in the middle.
If a departure from normality is detected, we transform the predicting variable to improve upon
the normality assumption. correct answers False
If a departure from the independence assumption is detected, we transform the response variable
to improve upon the independence assumption. correct answers False
The Box-Cox transformation is commonly used to improve upon the linearity assumption.
correct answers False
, In evaluating a simple linear model correct answers there is a direct relationship between the
coefficient of determination and the correlation between the predicting and response variables.
Goodness of fit assessment is done by correct answers residual analysis
R-squared (the coefficient of variation) is interpreted as correct answers the percentage of
variability in the response variable explained by the model.
The parameters of ANOVA are correct answers the k sample means and the population variance.
The pooled variance estimator is correct answers the sample variance estimator assuming equal
variances.
In ANOVA, the mean sum of squares divided by N-1 is correct answers the sample variance
estimator assuming equal means and equal variances.
MSE measures correct answers the within-treatment variability.
MSSTr measures correct answers the between treatment variability.
If we reject the test of equal means, we conclude that at least one pair of means are different.
correct answers True
If we do not reject the test of equal means, we conclude that means are definitely all equal.
correct answers False
If we reject the test of equal means, we conclude that all treatment means are not equal. correct
answers False
In ANOVA, the objective of residual analysis is to correct answers evaluate departures from the
model assumptions.
In ANOVA, the objective of the pairwise comparison is correct answers To identify the
statistically significant different means
For assessing the normality assumption of the ANOVA model, we can only use the quantile-
quantile normal plot of the residuals. correct answers False
The constant variance assumption is diagnosed using the histogram? correct answers False
The estimator sigma^2 is a random variable? correct answers True
The regression coefficients are used to measure the linear dependence between two variables?
correct answers False
