Effect of smaller variance

Multiple Linear Regression (MLR) Assumptions and Equations

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13 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
A smaller variance can sometimes overcompensate for omitted variable bias in a misspecified model.
A smaller variance always leads to more accurate predictions.
A smaller variance indicates a higher level of uncertainty in the data.
A smaller variance has no effect on model specification.
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Importance of MLR Assumptions
MLR assumptions ensure the efficiency and unbiasedness of OLS estimators.
MLR assumptions are only relevant for large sample sizes.
MLR assumptions guarantee the accuracy of all statistical models.
MLR assumptions are not necessary for regression analysis.
3.
MULTIPLE CHOICE QUESTION
3 mins • 1 pt
Multicollinearity
It occurs when independent variables in a regression model are highly correlated, making it difficult to isolate the individual effect of each variable.
It refers to the situation where dependent variables are correlated with each other.
It is a method used to increase the sample size in regression analysis.
It describes the relationship between the dependent variable and the independent variables in a linear regression model.
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Heteroskedasticity Impact
If heteroskedasticity is present, OLS is not the best estimator.
Heteroskedasticity improves the efficiency of OLS estimators.
Heteroskedasticity has no effect on OLS estimators.
OLS is always the best estimator regardless of heteroskedasticity.
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Error variance
A measure of the variability of the error term in a regression model.
A measure of the total variance in a dataset.
A technique used to minimize errors in data collection.
A statistical method for predicting future values.
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Trade-off between bias and variance
Bias will vanish as the sample size increases.
Variance increases with the complexity of the model.
Trade-off between bias and variance; bias will not vanish even in large samples.
High bias leads to overfitting the model.
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Estimated sampling variation of the estimated βj
se(β̂j) = √Var(β̂j) = √σ̂² / [SSTj(1 - R²j)]
se(β̂j) = σ̂² / [SSTj(1 + R²j)]
se(β̂j) = √(σ̂² / SSTj)
se(β̂j) = √(σ̂² * SSTj)
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