General Help with Econometric and R Software
"The Basics" - Section Week 1 - April 4th 2012 Topics: Estimating the Mean, When is an estimate of mean unbiased? Unbiased estimator. Variance of a random variable,
Installing and loading data with R software. Basic summary stats and histogram.
Section Week 2 - April 11th 2012 Topics: Population Variance, Sample Variance, Standard deviation, Estimating the variance. Adjusting for using the sample mean. Variance of estimate of mean (mu-hat). T-distribution. Inference using t-distribution
Central limit theorem, t-test (small samples), test-statistics (larger samples). Hypothesis testing. T-distribution table.
Homework 1 - due April 11th 2012 Expectations, mean, variance, and effect in non-systematic reporting error. R-softtware: basics, summary statistics, subsetting.
Section Week 3 - April 18th 2012 Topics: Inference about the location of the sample mean. T-statistic. Asymptotic results - the law of large numbers. The Central Limit Theorem
large sample test-statistics, hypothesis testing in R software.
Homework 2 - Due April 18th 2012 Standard error of the mean, determining bias of an estimate, small and large sample hypothesis testing, t-distribution and z-distribution, central limit theorem in action, In R-software: taking a sample of data, small and large sample hypothesis testing, taking multiple samples.
Mid-Term One Review - April 18th 2012Review of all material leading up to mid-term one. P-values. Regression, Ordinary Least Squares (OLS) in R software.
Section Week 5 - May 2nd 2012 Topics: Conditions under which OLS gives an unbiased estimate. "Proof" that OLS is unbiased under Simple Regression (SR) Assumptions. Assessing the assumptions.
Regression, Ordinary Least Squares (OLS) in R software. Pretty useful notes. Calculate a P-Value. "Prove" Ordinary Least Squares (OLS) regression coefficients (beta-hat-nought and beta-hat-one) minimize the squared distance between the dependent variable and the regression line. Plot, calculate OLS coefficients by hand, and interpret. Plot, calculate OLS coefficients in R, and interpret. Section Week 6 - May 10nd 2012 Topics: Calculating the bias. Variance of beta-hat-one. Variance of beta-hat-1 and inference.
Multivariate Regression in R. Normality assumption. R's linear model regression summary. Hypothesis testing with regression results. Finding and interpreting a regression's P-Value.
Homework 4 - due May 11th Derive variance of OLS intercept estimate. Regression, hypothesis testing and interpretation. Examination of regression assumptions required for inference.
Section Week 7 - May 17nd 2012 Topics: TSS: total sum of squares. ESS: explained sum of squared. RSS: sum of squared residuals. R-squared, goodness of fit. Motivation for multivariate regression. Estimation and interpretation.
Homework 5 - due May 18th
Derive multivariate coefficients. Multivariate regression in R. P-Values, R-squared. Derive effect of mean zero measurement error (attenuation bias). Measurement error in Data, example. - solutions (by Curtis) Problem 2 (R Code)
Multiple-variable regression. Level-level vs log-level regression. Interpretation, logging variables. Joint significance test, the F-test, plus interpretation. Normalizing variables and interpretation.
- solutions (pdf by Curtis)
Tip: F-Test critical value in R: qf(ConfLevel,dof_Numerator,dof_Denominator) CritVal <- qf(0.95,2,4852)
Final Exam Review - June 11th Previous Mid-Terms and Final Exams *All "solutions sketches" are quite sketchy, errors exist. - Sample Mid-Term 2004 ( pdf questions | solution sketch) 1) Calc the mean, dispersion metrics variance 2) z-table. probability of continuous random variable from a normal distribution. 3) Expected value of random variable (of a die) 4) OLS regression. Interpretation, zero conditional mean. EC) Interpreting regression result.
1) Mean, variance and correlation. Changes in scale. 2) z-table. probability of continuous random variable from a normal distribution. 3) Setting up a good study to run a regression on, unbiased assumptions. 4) Calc OLS regression, interpretation, zero conditional mean. EC) Conditional probability.
- Sample Mid-Term 2007 ( pdf questions | solution sketch) 1) Variance, co-variance and correlation. Changes in scale. 2) z-table. probability of continuous random variable from a normal distribution. 3) Calc OLS regression, interpretation, zero conditional mean. R-Squared. Omitted Variables. EC) Calculate Omitted Variable Bias.
- Sample Mid-Term 2009 ( pdf questions | solution sketch) 1) Given sample, find the covariance and correlation. 2) Calc OLS regression, interpretation, zero conditional mean. Hypothesis test. 3) Regression analysis. One-sided hypothesis test. Interpretation, zero conditional mean. EC) Prove that with regression assumptions, the regression coefficient is an unbiased estimate of beta-one. (univariate case).
- Sample Mid-Term 2010 ( pdf questions | solution sketch) 1) Calc OLS regression, plot, interpretation, r-squared, log-level interpretation, zero conditional mean assumption, bias. EC) Derive omitted variable bias.
- Sample Mid-Term 2011 Spring ( pdf questions | solution sketch) 1) Calc OLS regression. Hypothesis test, unbiased estimate?, practical significance. 2) Multivariate regression, hypothesis test, p-value, zero conditional mean and unbiasedness, direction of bias.
- Sample Mid-Term 2011 Summer ( pdf solutions, by S. Paterson) 1) Given sample, calc var, covariance and correlation. Calculate OLS regression coefficients. 2) z-table. probability of continuous random variable from a normal distribution. 3) Log-level multivariate regression. Interpret, hypothesis test. Assumptions that lead to unbiasedness, consistency. Practical significance. Omitted variable bias. EC) Derive OLS Regression coefficients.
- Sample Mid-Term 2010 Winter ( pdf questions) 1) Given sample, univariate regression estimation, plotting, bias and interpretation, prediction, R-squared & interpretation, log-level interpretation, zero conditional mean assumption & bias. EC) Omitted variable bias.
- Sample Mid-Term One 2012 Spring ( pdf questions | solution sketch) 1) Systematic measurement error and the mean. Unbiasedness of the mean with this measurement error. 2) Hypothesis testing, intuition, t-test vs z-test. 3) Expected value and probability, unfair coin. 4) R-Code.
- Sample Mid-Term Two 2012 Spring ( pdf questions | solution sketch) 1) Given sample data, churn out regression coefficient estimates, plot. 2) Univariate regression derivation with no intercept (algebra problem) 3) Zero conditional mean assumption, hypothesis test of statistical significance, interpretation, p-value, p-value interpretation, simple R-code.
1) Given sample, calc mean. z-table: probability of continuous random variable from a normal distribution. 2) Log-Log multivariate regression. Hypothesis test, interpretation, F-test. 3) Regression, hypothesis test, non-linear (quadratic) interpretation, p-value. 4) Multivariate regression, interpretation, prediction for a specific value, test of linear restrictions. 5) Unbiased estimator, consistent estimator, heteroskedasticity. 6) Test for heteroskedasticity, remidies. 7) Omitted variable bias. EC) Conditional probability.
1) z-table. probability of continuous random variable from a normal distribution. 2) Multivariate regression. Hypothesis test of statistical significance, one-sided test, interpretation of coefficient estimates, practical significance, R-squared interpretation, P-Value, non-linear quadratic model interpretation, resealing, F-test. 3) Multivariate regression interpretation, testing linear restrictions (delta method), zero conditional mean assumption, bias. EC) Probability question.
1) z-table. probability of continuous random variable from a normal distribution. 2) Multivariate regression. Hypothesis test of statistical significance, interpretation of coefficient estimates, R-squared interpretation, linear restriction and hypothesis test, non-linear quadratic model interpretation, F-test. 3) Multivariate log-level regression interpretation, testing linear restrictions (delta method), zero conditional mean assumption and bias. EC) biased estimate and consistent estimate.
1) Given sample, covariance and correlation. 2) Multivariate regression hypothesis testing, statistical significance, P-Value (plus illustration), non-linear quadratic model interpretation, practical significance, R-squared interpretation, interpretation of coefficients, F-test, zero conditional mean assumption, testing linear restrictions (delta method), testing for and dealing with heteroskedasticity.
1) Given sample, variance and correlation. 2) Setting up a regression. Sample bias, t-statistic hypothesis test, interpreting sources of bias. 3) Multivariate regression, one-sided hypothesis test, practical significance, P-Value, interpreting non-linear (quadratic) coefficient terms, interpret R-squared, statistical significance test, zero conditional mean assumption and bias, standardizing coefficients, test for and correct for heteroskedasticity. EC) Proof of unbiasedness of OLS Regression coefficients.
1) Univariate regression plot, and churn out coefficient estimates, interpretation, R-square interpretation, intercept regression, log-level regression interpretation, biased of regression estimates. 2) Regression hypothesis test of statistical significance, p-value calculation & interpretation, bias and zero conditional mean assumption, omitted variable bias and multivariate regression, practical significance, F-test of significance of multiple parameters, mean zero measurement error & attenuation bias.
1) Given sample data, derive univariate regression coefficient estimates, interpretation of regression results, plotting, bias and Gauss-Markov assumptions, interpretation & prediction of results, mean zero measurement error & attenuation bias. 2) Regression and unbiasedness assumptions, hypothesis test of statistical significance, p-value calculation and interpretation, F-test of statistical significance of multiple parameters, interaction terms hypothesis test, altering regression to calculate standard error of a prediction.
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