# pq1 - Practice Questions for Midterm 1 Introduction to...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Practice Questions for Midterm 1 Introduction to Econometrics - Fall 2006 1. The random variables X and Y are related by the following relationship: Y = a + bX: Show that corr ( X;Y ) = 1 if b &gt; and corr ( X;Y ) = &amp; 1 if b &lt; . 2. The distribution of the temperature in Madison is characterized by parameter &amp; . The value of &amp; is unknown. However, we know it &amp; = 1 . After several measurements of the weather, an estimator ^ &amp; is obtained. It is known that ^ &amp; can only take 4 possible values. Given that the true value of the parameter is &amp; = 1 , the likelihood of each value of ^ &amp; is given in the following table: ^ &amp; 1 2 3 Pr [^ &amp; ] : 20 : 50 : 25 : 05 For instance, Pr [^ &amp; = 2] = 0 : 25 . (a) Write the cumulative distribution of ^ &amp; and show it on a graph. (b) Suppose that you obtain an estimate ^ &amp; = 3 Given the distribution for ^ &amp; , would you reject the null hypothesis that &amp; = 1 at a 90% con&amp;dence level? Explain. (c) Suppose that you obtain an estimate ^ &amp; = 2 Given the distribution for ^ &amp; , would you reject the null hypothesis that &amp; = 1 at a 90% con&amp;dence level? Explain. (d) Compute the mean and the variance of ^ &amp; . Is ^ &amp; a biased estimator of &amp; ? 3. You want to study the relationship between the level of education of a person and his/her parents income. (a) You decide to consider the following linear regression model: edu i = + 1 inc i + u i where E ( u i j inc i ) = 0 : In this model, edu i is the number of years individual i went to school and inc i is the average annual income (measured in thousand of dollars) of his/her parents in the &amp;rst 25 years of his/her life. You use the simple random sampling scheme to obtain a sample of 5000 observation from the population and from this sample you obtain the following OLS regression line. d edu i = b + b 1 inc i Are the three least squares assumption holding? What does this imply in terms of unbiasedness and consistency of the OLS estimators b and b 1 ? What is the distribution of b and b 1 ? (b) Now you decide to consider an alternative linear regression model: edu i = alt 1 inc i + u alt i Using the same sample as in a., you obtain the following OLS regression line: d edu i = b alt 1 inc i Are the three least squares assumption holding? What does this imply in terms of unbiasednessAre the three least squares assumption holding?...
View Full Document

## This note was uploaded on 07/28/2010 for the course ECON 410 taught by Professor Staff during the Fall '08 term at Wisconsin.

### Page1 / 4

pq1 - Practice Questions for Midterm 1 Introduction to...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online