Kinh tế học - Chapter 4: Basic estimation techniques

Chapter 4Basic Estimation TechniquesSimple Linear Regression Simple linear regression model relates dependent variable Y to one independent (or explanatory) variable X• Slope parameter (b) gives the change in Y associated with a one-unit change in X, 2Method of Least Squares The sample regression line is an estimate of the true regression line ••3Sample Regression Line (Figure 4.2)A08,0002,00010,0004,0006,00010,00020,00030,00040,00050,00060,00070,000Advertising expenditures (dollars)Sales (dollars)S•••••••ei4The distribution of values the estimates might take is centered around the true value of the parameterAn estimator is unbiased if its average value (or expected value) is equal to the true value of the parameterUnbiased Estimators••5Relative Frequency Distribution* (Figure 4.3)0821046113579*Also called a probability density function (pdf)6Must determine if there is sufficient statistical evidence to indicate that Y is truly related to X (i.e., b  0)Statistical Significance•Test for statistical significance using t-tests or p-values7First determine the level of significanceProbability of finding a parameter estimate to be statistically different from zero when, in fact, it is zeroProbability of a Type I Error1 – level of significance = level of confidencePerforming a t-Test8Performing a t-TestUse t-table to choose critical t-value with n – k degrees of freedom for the chosen level of significancen = number of observationsk = number of parameters estimated•9Performing a t-TestIf absolute value of t-ratio is greater than the critical t, the parameter estimate is statistically significant10Using p-ValuesTreat as statistically significant only those parameter estimates with p-values smaller than the maximum acceptable significance levelp-value gives exact level of significanceAlso the probability of finding significance when none exists11Coefficient of DeterminationR2 measures the percentage of total variation in the dependent variable that is explained by the regression equationRanges from 0 to 1High R2 indicates Y and X are highly correlated12F-TestUsed to test for significance of overall regression equationCompare F-statistic to critical F-value from F-tableTwo degrees of freedom, n – k & k – 1Level of significanceIf F-statistic exceeds the critical F, the regression equation overall is statistically significant13Multiple RegressionUses more than one explanatory variableCoefficient for each explanatory variable measures the change in the dependent variable associated with a one-unit change in that explanatory variable14Use when curve fitting scatter plotQuadratic Regression Models•••is U-shaped or U -shaped 15Log-Linear Regression Models•••••16