ISYE 6414 Regression Modules 1-2 |
2024 Questions & Answers | 100%
Correct | Verified
Assuming that the data are normally distributed, under the simple linear model, the estimated variance
has the following sampling distribution: - ✔✔Chi-squared with n-2 degrees of freedom.
The fitted values are defined as? - ✔✔The regression line with parameters replaced with the estimated
regression coefficients.
The estimators fo the linear regression model are derived by? - ✔✔Minimizing the sum of squared
differences between the observed and expected values of the response variable.
The estimators for the regression coefficients are: - ✔✔Unbiased regardless of the distribution of the
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 can only be used to assess uncorrelated errors. - ✔✔False
Independence assumption can be assess using the normal probability plot. - ✔✔False
Independence assumption can be assessed using the residuals vs fitted values. - ✔✔False
, We detect departure from the assumption of constant variance - ✔✔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. - ✔✔False
If a departure from the independence assumption is detected, we transform the response variable to
improve upon the independence assumption. - ✔✔False
The Box-Cox transformation is commonly used to improve upon the linearity assumption. - ✔✔False
In evaluating a simple linear model - ✔✔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 - ✔✔residual analysis
R-squared (the coefficient of variation) is interpreted as - ✔✔the percentage of variability in the
response variable explained by the model.
The parameters of ANOVA are - ✔✔the k sample means and the population variance.
The pooled variance estimator is - ✔✔the sample variance estimator assuming equal variances.
In ANOVA, the mean sum of squares divided by N-1 is - ✔✔the sample variance estimator assuming
equal means and equal variances.
MSE measures - ✔✔the within-treatment variability.
MSSTr measures - ✔✔the between treatment variability.
2024 Questions & Answers | 100%
Correct | Verified
Assuming that the data are normally distributed, under the simple linear model, the estimated variance
has the following sampling distribution: - ✔✔Chi-squared with n-2 degrees of freedom.
The fitted values are defined as? - ✔✔The regression line with parameters replaced with the estimated
regression coefficients.
The estimators fo the linear regression model are derived by? - ✔✔Minimizing the sum of squared
differences between the observed and expected values of the response variable.
The estimators for the regression coefficients are: - ✔✔Unbiased regardless of the distribution of the
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 can only be used to assess uncorrelated errors. - ✔✔False
Independence assumption can be assess using the normal probability plot. - ✔✔False
Independence assumption can be assessed using the residuals vs fitted values. - ✔✔False
, We detect departure from the assumption of constant variance - ✔✔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. - ✔✔False
If a departure from the independence assumption is detected, we transform the response variable to
improve upon the independence assumption. - ✔✔False
The Box-Cox transformation is commonly used to improve upon the linearity assumption. - ✔✔False
In evaluating a simple linear model - ✔✔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 - ✔✔residual analysis
R-squared (the coefficient of variation) is interpreted as - ✔✔the percentage of variability in the
response variable explained by the model.
The parameters of ANOVA are - ✔✔the k sample means and the population variance.
The pooled variance estimator is - ✔✔the sample variance estimator assuming equal variances.
In ANOVA, the mean sum of squares divided by N-1 is - ✔✔the sample variance estimator assuming
equal means and equal variances.
MSE measures - ✔✔the within-treatment variability.
MSSTr measures - ✔✔the between treatment variability.
