Lecture 3: Hypothesis Testing (Part I)

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Questions and Answers

What are the two hypotheses used in hypothesis testing?

Primary hypothesis and secondary hypothesis

Initial hypothesis and final hypothesis

Hypothesis A and Hypothesis B

Null hypothesis and alternative hypothesis (correct)

What are the two hypotheses used in hypothesis testing?

Null hypothesis and test hypothesis (correct)

Alternative hypothesis and test hypothesis

Alternative hypothesis and research hypothesis

Null hypothesis and research hypothesis

What are the two hypotheses used in hypothesis testing?

Null hypothesis and test hypothesis (correct)

Alternative hypothesis and test hypothesis

Alternative hypothesis and research hypothesis

Null hypothesis and research hypothesis

What does the coefficient's standard error measure?

The reliability of a point estimate Signup and view all the answers

What does the coefficient's standard error measure?

The reliability of a point estimate Signup and view all the answers

What is the purpose of the coefficient's standard error in measuring the reliability of a point estimate?

To assess the precision of the point estimate Signup and view all the answers

When is the t-distribution used in hypothesis testing?

When the variance of the disturbances is estimated Signup and view all the answers

When is the t-distribution used in hypothesis testing?

When the variance of the disturbances is estimated Signup and view all the answers

Which approaches can be used to conduct a hypothesis test?

Test of significance and F-test Signup and view all the answers

When is the t-distribution used in hypothesis testing?

When the variance of the disturbances is estimated Signup and view all the answers

Are confidence intervals always one-sided?

No Signup and view all the answers

Are confidence intervals always one-sided?

No Signup and view all the answers

Do the test of significance and confidence interval approaches always give the same answer?

Yes Signup and view all the answers

Do the test of significance and confidence interval approaches always give the same answer?

Yes Signup and view all the answers

Are confidence intervals always one-sided or two-sided?

Two-sided Signup and view all the answers

What is the conventionally set significance level?

5% Signup and view all the answers

Do the test of significance and confidence interval approaches always give the same answer?

Yes Signup and view all the answers

What is the conventionally set significance level?

5% Signup and view all the answers

What is the F-test used for?

To test multiple hypotheses simultaneously Signup and view all the answers

What is the conventionally set significance level in hypothesis testing?

5% Signup and view all the answers

What is the F-test used for?

To test multiple hypotheses simultaneously Signup and view all the answers

What is the F-test used for in hypothesis testing?

To test multiple hypotheses simultaneously Signup and view all the answers

What is the test statistic for the F-test calculated using?

RRSS, URSS, T, k, and m Signup and view all the answers

What is the test statistic for the F-test calculated using?

RRSS, URSS, T, k, and m Signup and view all the answers

What is R2?

A goodness of fit statistic Signup and view all the answers

What is R2?

A goodness of fit statistic Signup and view all the answers

What is R2 used for in regression analysis?

To measure how well the regression model fits the data Signup and view all the answers

What does adjusted R2 take into account?

The loss of degrees of freedom associated with adding extra variables Signup and view all the answers

What is the formula for adjusted R2?

1 - [(T-1)/(T-k)(1-R2)] Signup and view all the answers

What does adjusted R2 take into account?

The loss of degrees of freedom associated with adding extra variables Signup and view all the answers

Study Notes

The lecture covers hypothesis testing in econometrics.
Two hypotheses are always used in hypothesis testing: null hypothesis and alternative hypothesis.
The null hypothesis is the statement being tested, and the alternative hypothesis represents the remaining outcomes of interest.
The reliability of a point estimate is measured by the coefficient's standard error.
The test of significance and confidence interval approaches can be used to conduct a hypothesis test.
The t-distribution is used in hypothesis testing when the variance of the disturbances is estimated.
Confidence intervals are almost always two-sided.
The test of significance and confidence interval approaches always give the same answer.
The significance level is conventionally set at 5%, but 10% and 1% are also commonly used.
The lecture provides an example of how to conduct a hypothesis test using both the test of significance and confidence interval approaches.

The text discusses hypothesis testing using the test of significance approach and confidence interval approach.
The hypotheses are presented as H0 and H1.
The F-test is used to test multiple hypotheses simultaneously.
The t-ratio test is used to test single hypotheses involving one coefficient.
The F-test involves estimating both restricted and unrestricted regressions.
The test statistic for the F-test is calculated using RRSS, URSS, T, k, and m.
The F-distribution is used to determine the critical value for rejecting the null hypothesis.
The t-distribution is a special case of the F-distribution.
The text emphasizes the importance of caution when making decisions in marginal cases.
A statistically significant result may not necessarily be of practical significance.
Restricted regression formula is given as zt = β1 + β4x4t + ut.
F-test statistic is used to test the significance of the regression model.
Data mining is the process of searching for statistical relationships without theoretical justification.
Goodness of fit statistics are used to measure how well the regression model fits the data.
R2 is the most common goodness of fit statistic.
R2 is defined as the ratio of explained sum of squares to total sum of squares.
R2 must always lie between zero and one.
Adjusted R2 takes into account the loss of degrees of freedom associated with adding extra variables.
Adjusted R2 is given as 1 - [(T-1)/(T-k)(1-R2)].
Chapters 3 and 4 of Chris Brooks' Introductory Econometrics for Finance and Chapter 4 of Jeffrey Wooldridge's Introductory Econometrics are essential readings.