Regression Analysis Concepts Quiz

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to Lesson

Podcast

Play an AI-generated podcast conversation about this lesson
Download our mobile app to listen on the go
Get App

Questions and Answers

What is the consequence of omitting an important variable from a regression analysis?

  • The coefficient estimates will remain unbiased.
  • The standard errors will become more accurate.
  • The estimated coefficients will be biased and inconsistent. (correct)
  • All other variable coefficients will be consistent.

What is the main assumption behind the parameter stability tests?

  • The model must include at least three independent variables.
  • Data must be collected over multiple years.
  • Parameters are constant for the entire sample period. (correct)
  • Coefficient estimates are not affected by sample size.

In the Chow test, what is used to form the F-test?

  • Difference between the sum of squared residuals (RSS) of the regressions. (correct)
  • Difference between the means of the sub-periods.
  • The estimated variance of the error term.
  • The total number of observations in the sample.

What happens if an irrelevant variable is included in a regression model?

<p>The estimators will be inefficient but unbiased. (C)</p> Signup and view all the answers

When creating a dummy variable, what is the purpose of setting it to zero otherwise?

<p>To isolate the effect of a specific observation. (A)</p> Signup and view all the answers

What is the null hypothesis in the Goldfeld-Quandt test?

<p>$H_0: ext{Var}( ext{ disturbances})$ are equal (C)</p> Signup and view all the answers

When conducting the GQ test, what is the next step after splitting the sample into two sub-samples?

<p>Estimate the regression model on both sub-samples (C)</p> Signup and view all the answers

What is the formula for the GQ test statistic?

<p>$GQ = rac{s^2_{ ext{larger}}}{s^2_{ ext{smaller}}}$ (C)</p> Signup and view all the answers

In White's Test, what is the purpose of running the auxiliary regression?

<p>To obtain residuals that will test for heteroscedasticity (B)</p> Signup and view all the answers

What distribution does the test statistic from the GQ test follow under the null hypothesis?

<p>F-distribution (D)</p> Signup and view all the answers

Why might the choice of where to split the sample in the GQ test be problematic?

<p>The outcome of the test can vary based on the split location. (A)</p> Signup and view all the answers

How is the chi-squared statistic calculated in White’s test after running the auxiliary regression?

<p>By multiplying R2 by the number of observations, T (C)</p> Signup and view all the answers

What is indicated by the null hypothesis in the Breusch-Godfrey Test?

<p>There is no autocorrelation present. (D)</p> Signup and view all the answers

What is the consequence of ignoring autocorrelation in a regression model?

<p>The standard error estimates become inappropriate. (C)</p> Signup and view all the answers

Which statement is true regarding the method to correct for autocorrelation when its form is known?

<p>GLS procedures may introduce additional assumptions. (B)</p> Signup and view all the answers

What is a key characteristic of perfect multicollinearity?

<p>Some explanatory variables are perfectly correlated. (C)</p> Signup and view all the answers

In the analysis of autocorrelation, what is the significance of the test statistic exceeding the critical value?

<p>It indicates a rejection of the null hypothesis. (C)</p> Signup and view all the answers

What does it mean when R2 is inflated due to positively correlated residuals?

<p>The perceived explanatory power of the model is overstated. (A)</p> Signup and view all the answers

What is a potential problem if near multicollinearity is present but ignored?

<p>Standard errors of the coefficients may become high. (A)</p> Signup and view all the answers

Which analysis method can be used when the form of autocorrelation is unknown?

<p>Modify the regression model based on residual analysis. (B)</p> Signup and view all the answers

What is the outcome if a regression model is estimated under conditions of perfect multicollinearity?

<p>No individual coefficients can be estimated. (C)</p> Signup and view all the answers

What is a characteristic of regression analysis when multicollinearity is present?

<p>Confidence intervals for parameters become wide. (D)</p> Signup and view all the answers

Which method is NOT commonly used to measure multicollinearity?

<p>Standard deviation of residuals. (C)</p> Signup and view all the answers

What is one suggested solution to address multicollinearity?

<p>Increase the frequency of data collection. (C)</p> Signup and view all the answers

What is a potential solution if the true model is a non-linear model?

<p>Transform the data into logarithms. (C)</p> Signup and view all the answers

Which statistical test can be used to check for functional form mis-specification in a regression model?

<p>Ramsey’s RESET test. (A)</p> Signup and view all the answers

What happens if the value of the test statistic in Ramsey’s RESET test exceeds the critical value?

<p>Reject the null hypothesis. (C)</p> Signup and view all the answers

What do skewness and kurtosis measure in a distribution?

<p>The distribution's shape characteristics. (B)</p> Signup and view all the answers

What is a common misconception about high correlation between one of the independent variables and the dependent variable?

<p>It indicates multicollinearity. (A)</p> Signup and view all the answers

Which test formalizes checking the normality of residuals?

<p>Bera Jarque test. (B)</p> Signup and view all the answers

What is the coefficient of kurtosis for a normal distribution?

<p>3 (B)</p> Signup and view all the answers

Which of the following is likely a drawback of traditional solutions for multicollinearity?

<p>They often cause more problems than they solve. (A)</p> Signup and view all the answers

What does the Bera Jarque test statistic W need to be transformed into?

<p>Chi-square distribution. (D)</p> Signup and view all the answers

What is the purpose of including higher order terms in the auxiliary regression of Ramsey's RESET test?

<p>To examine potential mis-specification of functional form. (B)</p> Signup and view all the answers

When residuals exhibit non-normality, what is a common course of action?

<p>Use dummy variables. (C)</p> Signup and view all the answers

When transforming highly correlated variables into ratios, what is the intended outcome?

<p>To reduce the number of variables without losing information. (D)</p> Signup and view all the answers

What is one consequence of multicollinearity that affects statistical tests?

<p>Standard errors of coefficients increase. (A)</p> Signup and view all the answers

What indicates the rejection of the normality assumption in residuals?

<p>Presence of extreme residuals. (A)</p> Signup and view all the answers

In the context of hypothesis testing, why is normality assumed?

<p>It simplifies the calculation of probabilities. (D)</p> Signup and view all the answers

What do the coefficients of skewness and kurtosis indicate when they are jointly tested for normality?

<p>They must equal zero for normality. (C)</p> Signup and view all the answers

What is the commonly used method to test for departures from normality?

<p>Shapiro-Wilk test. (D)</p> Signup and view all the answers

Flashcards

Heteroscedasticity Test

A statistical test used to check if the variance of the error terms in a regression model is constant across different levels of the independent variables. It tests whether the spread of the data points around the regression line is the same across all values of the independent variable.

Goldfeld-Quandt (GQ) Test

A statistical test used to detect heteroscedasticity in a regression model. It involves splitting the sample data into two groups and comparing the variances of the residuals calculated from each group.

White's Test

A statistical test used to detect heteroscedasticity in a regression model. This test is more adaptable to different forms of heteroscedasticity and doesn't rely on specific assumptions about the pattern of heteroscedasticity.

Residuals

The difference between the actual observed values of the dependent variable and the values predicted by the regression model.

Signup and view all the flashcards

Heteroscedasticity

The variance of the residuals in a regression model is not constant but changes across different values of the independent variables. This means the spread of data points around the regression line varies for different values of the independent variables.

Signup and view all the flashcards

Homoscedasticity

A regression model where the error terms have constant variance across all values of the independent variables.

Signup and view all the flashcards

Error Term Variance

The variance of the error term in a regression model. It indicates the spread of the data points around the regression line.

Signup and view all the flashcards

Breusch-Godfrey Test

It is a statistical test to check for rth order autocorrelation, testing if residuals are correlated with themselves at different lags.

Signup and view all the flashcards

Multicollinearity

A situation where explanatory variables in a regression model are highly correlated with each other, leading to problems in estimating individual coefficients.

Signup and view all the flashcards

Perfect Multicollinearity

A situation where explanatory variables are perfectly linearly related. It makes it impossible to estimate all model coefficients.

Signup and view all the flashcards

Near Multicollinearity

When explanatory variables are highly correlated but not perfectly, causing issues in estimating individual coefficients, leading to high standard errors.

Signup and view all the flashcards

Autocorrelation (in Regression)

The presence of autocorrelation, where residuals are correlated with each other at different lags, can lead to various issues in regression analysis.

Signup and view all the flashcards

Generalized Least Squares (GLS)

A statistical approach that estimates model coefficients while taking into account autocorrelated residuals.

Signup and view all the flashcards

Cochrane-Orcutt Method

A method used to correct for autocorrelation in time series data, based on the assumption of a specific autocorrelation model, such as an AR(1).

Signup and view all the flashcards

Consequences of Ignoring Autocorrelation

In regression, if autocorrelation is ignored, even though OLS estimates remain unbiased, they are inefficient, causing problems in inferences and potentially inflated R2 values.

Signup and view all the flashcards

Residual Autocorrelation

It refers to a situation when residuals in a time series model are correlated with their past values, and this correlation is not random.

Signup and view all the flashcards

What are dummy variables?

A dummy variable is a binary variable that takes a value of 1 if a certain condition is met, and 0 otherwise. They are used to account for qualitative factors in regression analysis, which cannot be measured directly. For example, a dummy variable could be created to represent a gender (1 for female, 0 for male).

Signup and view all the flashcards

Omission bias

This type of bias occurs when an important explanatory variable is omitted from the regression model. This can lead to incorrect or misleading results, as the estimates for the included variables will be influenced by the missing variable.

Signup and view all the flashcards

Inclusion bias

If an irrelevant variable is included in the regression model, it will not impact the consistency and unbiasedness of the estimates for other variables. However, the efficiency of the model will be reduced, leading to less precise results.

Signup and view all the flashcards

Chow test

The Chow test is a statistical test used to determine if the parameters of a regression model are stable over different time periods. It helps analyze whether the relationship between variables remains consistent for the entire dataset or if it shifts across different intervals.

Signup and view all the flashcards

Predictive failure tests

It aims to check if the predictions from a model trained on one part of the data are accurate for the other part. It helps assess the model's ability to generalize to new data and identify possible parameter instability.

Signup and view all the flashcards

Bera Jarque Normality Test

A statistical test that checks if the distribution of residuals in a regression model is normal.

Signup and view all the flashcards

Skewness

A measure of the asymmetry of a distribution. A positive skewness indicates a long right tail, while a negative skewness indicates a long left tail.

Signup and view all the flashcards

Kurtosis

A measure of the peakedness of a distribution. A high kurtosis indicates a sharp peak with heavy tails, while a low kurtosis indicates a flatter peak with lighter tails.

Signup and view all the flashcards

Coefficient of Skewness (b1)

The third standardized moment of a distribution, measuring its skewness.

Signup and view all the flashcards

Coefficient of Excess Kurtosis (b2-3)

The fourth standardized moment of a distribution, measuring its kurtosis, but adjusted so that the normal distribution has a kurtosis of 3.

Signup and view all the flashcards

Bera Jarque Test

A statistical test used to determine whether the distribution of residuals from a regression model is significantly different from a normal distribution.

Signup and view all the flashcards

Bera Jarque Test Statistic (W)

A test statistic used in the Bera Jarque test for normality. It is calculated using the coefficients of skewness and kurtosis from the residuals.

Signup and view all the flashcards

Dummy Variables for Outliers

The use of dummy variables to account for outliers in a regression model.

Signup and view all the flashcards

Non-Parametric Methods

A statistical method that does not assume normality in the data.

Signup and view all the flashcards

Correlation Matrix

A simple way to detect multicollinearity by looking at the correlation coefficients between independent variables. High correlations (above 0.8) suggest possible multicollinearity.

Signup and view all the flashcards

Variance Inflationary Factor (VIF)

A measure of how much the variance of a regression coefficient is inflated due to multicollinearity. A VIF greater than 10 suggests strong multicollinearity.

Signup and view all the flashcards

Dropping a Variable

Removing one of the highly correlated variables from the regression model.

Signup and view all the flashcards

Variable Ratio

Combining two or more highly correlated variables into a single ratio, reducing the collinearity.

Signup and view all the flashcards

Ramsey's RESET Test

A statistical test that checks whether the chosen functional form (e.g., linear) is correct. It adds higher-order terms of the fitted values to an auxiliary regression.

Signup and view all the flashcards

Mis-specification of Functional Form

It's possible that the true relationship between variables is not linear. This test helps you discover if the assumed linear model is appropriate.

Signup and view all the flashcards

Regression Residuals

The residuals of a regression model are the differences between the actual observed values of the dependent variable and the values predicted by the model. These residuals are used in various statistical tests to assess the model's performance.

Signup and view all the flashcards

Ramsey's RESET Test

A general test for mis-specification, it adds higher order terms of fitted values to a regression.

Signup and view all the flashcards

Adding More Data

Collecting more data points can sometimes help reduce the problem of multicollinearity, especially if you have a longer time frame or collect data at a higher frequency.

Signup and view all the flashcards

Study Notes

Classical Linear Regression Model Assumptions and Diagnostics

  • Classical linear regression models (CLRM) have assumptions for disturbance terms.
  • These assumptions include:
    • Expected value of the error term (εt) is zero (E(εt) = 0).
    • Variance of the error term is constant (Var(εt) = σ2).
    • Covariance between any two error terms is zero (cov(εi, εj) = 0 for i ≠ j).
    • The X matrix is non-stochastic or fixed in repeated samples.
    • Errors are normally distributed (εt ~ N(0, σ2)).

Violations of CLRM Assumptions

  • Studying violations of assumptions, including how to test for them, their causes, and consequences.
  • Consequences can include incorrect coefficient estimates, inaccurate standard errors, and inappropriate test statistics.
  • Solutions involve addressing violations or employing alternative techniques.

Assumption 1: E(εt) = 0

  • The mean of the disturbances is assumed to be zero.
  • Residuals are used to test this assumption, and their mean will always be zero if there's a constant term in the regression.

Assumption 2: Var(εt) = σ2

  • Homoscedasticity - the variance of errors is constant (Var(εt) = σ2)
  • Heteroscedasticity - the variance of errors varies.
    • Detection includes methods like the Goldfeld-Quandt (GQ) test and White's test.
    • The GQ test involves splitting the data, calculating residual variances, and forming a ratio for the test statistic following an F distribution.
    • White's test uses an auxiliary regression based on squared residuals and regressors.

Consequences of Heteroscedasticity

  • Using OLS with heteroscedasticity leads to unbiased coefficient estimates, but standard errors are wrong and inferences are flawed.
  • The degree of bias in standard errors depends on the form of heteroscedasticity.

Dealing with Heteroscedasticity

  • If the form of heteroscedasticity is known, generalized least squares (GLS) can be used.
  • A simple illustration of GLS divides the regression by a variable related to the error variance .

Autocorrelation

  • The CLRM assumes no pattern, or zero covariance, between errors (Cov(εi, εj) = 0).
  • If errors have patterns, they're autocorrelated.
    • Detecting autocorrelation (formal tests, such as Durbin-Watson, and Breusch-Godfrey test)
    • Durbin-Watson Test (DW) tests for first-order autocorrelation, comparing errors with prior errors; ranges from 0 to 4.
    • Breusch-Godfrey test is a more general, rth-order autocorrelation test.

Consequences of Ignoring Autocorrelation

  • Coefficient estimates remain unbiased but are inefficient (not BLUE).
  • Standard errors are inappropriate and often lead to incorrect inferences, such as incorrect conclusions about variable significance.
  • R-squared values can be inflated in the presence of positively autocorrelated errors.

Remedies for Autocorrelation

  • GLS techniques can be employed if the form of autocorrelation is known.
  • Procedures like Cochrane-Orcutt are examples of GLS when autocorrelations are evident.
  • Often modify the regression to fix autocorrelation if its form cannot be identified.

Multicollinearity

  • High correlations between explanatory variables.
  • Perfect multicollinearity renders coefficient estimation impossible.
  • Near multicollinearity impacts coefficient standard errors (making them large) and sensitivity of the regression to specification changes.
  • R-squared is often high but individual variables become less significant when multicollinearity is present.

Measuring Multicollinearity

  • Method 1: Assessing the correlations between variables using a correlation matrix.
  • Method 2: Analyzing the variance inflation factors (VIFs) to measure the effect of multicollinearity on independent variables.

Solutions to Multicollinearity

  • Traditional techniques like ridge regression or principal component analysis.
  • Some practitioners opt to ignore the issue if the model's validity is otherwise well-supported.
  • Drop one of the collinear variables or transform the variables into ratios, or seek more data.

Incorrect Functional Form

  • If the relationship between variables is not linear.
  • Ramsey's RESET test can be used to identify non-linearity.
  • This test adds higher powers of fitted values to an auxiliary regression to assess if the linearity assumption is valid by examining the R squared from the auxiliary regression.

Testing Normality

  • Normality assumption implies errors are normally distributed.
  • Bera-Jarque test is used, assessing skewness (b1) and kurtosis (b2); a normal distribution has zero skewness and a kurtosis of 3 (b2 = 3). A jointly zero result confirms theoretical normality.
  • The test statistic is a function of these coefficients, and a large value suggests non-normality.

Solutions for Non-Normality

  • Switch to a non-parametric method if normality tests produce rejection.
  • Identify and consider transformations to handle non-normality or errors that are too extreme and use dummy variables for identified extreme errors.

Omission of an Important Variable or Inclusion of an Irrelevant Variable

  • Omitting relevant variables leads to biased coefficient estimates in other variables.
  • Including irrelevant variables increases the number of variables without improving analysis effectiveness.

Parameter Stability Test

  • Assesses whether parameters in a model remain constant over the entire sample or just parts of the sample.
  • Chow test is a common technique for analyzing parameter stability, essentially comparing restricted and unrestricted models.
  • This approach performs a separate regression for the whole period, and each sub-part. An F ratio compares the restricted to unrestricted model.
  • If the statistic exceeds the critical value, you reject the null hypothesis that the parameters are unchanging.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Quiz Team

Related Documents

CLRM Assumptions & Diagnostics PDF

More Like This

Use Quizgecko on...
Browser
Open
Browser
Browser