# ECON 220

 Point estimator is a sample statistic U used to provide a one-point approximation to the value of an unknown parameter θ. Sampling Error is given by the absolute value of the difference between the estimated value and true value of the parameter of interest. | U-θ | Geometrically: Sampling error measures the distance between the two points U and θ. Unbiased Estimator U attempting to estimate θ such that E(U) = θ. Bias E(U) - θ More efficient Suppose U and W are two unbiased estimators for θ. Then U is ___________ provided that it has a smaller variance. Relative Efficiency of U to W:100[V(W)/V(U)] Confidence Level the percentage 100(1-α)% Confidence Interval Sample Mean ± Critical Value * Standard Error Margin of Error limit on the size of sampling error.P(sampling errorinfinity T-Distribution congergys to... standard normal distribution as df-->infinity Small Sample Confidence Interval- Assumptions VSRSnormal populationσ is unknown Small Sample Confidence Interval for the Mean- Calculations xbar ± tα/2 (s/√n) Large Sample Confidence Interval for the Proportion- Assumptions Binomial PopulationVSRSn is sufficiently large (np≥5, n(1-p)≥5) Large Sample Confidence Interval for the Proportion- Calculation pbar ± Zα/2 (√pbar(1-pbar)/n) Null Hypothesis statement about the population of interest. Alternative Hypothesis statement about the populatin of interest that contradicts the null hypothesis. Test Statistic sample statistic that is used to summarize the evidence. Significance probability of making an error in judgement. Fisher's Theory (Heuristic) The P-value is the probability of observing a value of the test statistic "at least as extreme as" what was actually observed. -focuses on type I error (false positive) Interpreting P-Values the P-velue is computed by temporarily assuming the null hypothesis is true. a low P-value casts doubt upon the assumption that the null hypothesis is true. Thus, we reject it. a high P-value is consistent with the assumption that the null hypothesis is true. Thus, we do not reject it. Neyman-Pearson Theory power calculations the p-value is the smallest significance level for which the null hypothesis can be rejected. Type I Error false positive Type II Error false negative Decision Rule specifies the set of values of the test statistic for which the null hypothesis is rejected in favor of the alternative hypothesis and the set of values for which the null hypothesis is accepted. Rejection Region consists of all values of the test statistic for which the null hypothesis is rejected. Acceptance Region consists of all values of the test statistic for which the null hypothesis is accepted. Critical Value value that separates the rejection region from the acceptance region. Power 1-B where B is the probability of making type II error Large Sample Hypothesis Test for the Proportion- Assumptions Binomial PopulationVSRSn is sufficiently large (based on null hypothesis value of p) Large Sample Confidence Interval for the Proportion- Calculations z=pbar-pnot/(√pnot(1-pnot)/n) P-Value probability of observing a value of the test statistic "at least as extreme as" what was actually observed.the p-value is the smallest significance level for which the null hypothesis can be rejected.**p-value is the observed significance level** Regression Statistics- Multiple R positive square root of R Square. Large value indicates a good fit. Regression Statistics-R Square number indicates that ___% of the variation in the response variable Y is explained by its linear relationship with the explanatory variable X. Regression Statistics-Adjusted R Square adjustement of R Square for degrees of freedom. The adjustment serves as a penalty for using too many explanatory variables. Regression Statistics-Standard Error "Standard Error of Regression" and estimates the standard deviation of the error specification in the model. A relatively small standard error is another indication of a good fit. ANOVA- First Column "Regression" always refers to the part that is explained and "Residual" to the part that is unexplained. The "Total" is typically the sum of the explained and unexplained components, wherever this way of thinking is useful. ANOVA- Second Column analyzes degrees of freedom. The total degrees of freedom is always n-1. If there is only one explanatory variable, Regression df=1. The Residual degrees of freedom is what is left over (ie: 19-1=18). ANOVA- Third Column analyzes the variation in the response variable in terms of Sum of Squares. The Total Sum of Squares is simply the sum of the squared deviations from the sample mean for Y. The Regression SS is the variation in the response variable Y that is explained byt he regression line. Residual SS is interpreted as the variation in the response variable Y that is not explained by the linear regression line. ANOVA- Fourth Column Mean Square is a Sum of Squares divided by the appropriate degrees of freedom. It is easy to check that the square root of the Residual MS is equal to the Standard Error of Regression listed in the Regression Statistics. ANOVA- Fifth Column F-Statistic is the ratio of MS Regression to MS Residual. Large value of F supports the alternative hypothesis that the linear regression model fits the data against the null hypothesis that the linear regression model does not fit the data. Authorjlmoor6 ID16291 Card SetECON 220 DescriptionECON 220- Statistical Methods in Economics Updated2010-04-28T17:33:08Z Show Answers