tailieunhanh - Lecture Managerial economics (9th edition): Chapter 4 – Thomas, Maurice

Chapter 4 - Basic estimation techniques. After completing this unit, you should be able to: Set up a regression equation that can be estimated using a computerized regression routine, interpret and understand how to use the computer output to investigate problems that are of interest to managers of a firm, specify a relation or model between a dependent variable and the appropriate independent variable(s) that can be estimated using regression techniques,. | Chapter 4 Basic Estimation Techniques Simple 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, 4- Method of Least Squares The sample regression line is an estimate of the true regression line • • 4- Sample Regression Line (Figure ) A 0 8,000 2,000 10,000 4,000 6,000 10,000 20,000 30,000 40,000 50,000 60,000 70,000 Advertising expenditures (dollars) Sales (dollars) S • • • • • • • ei 4- The distribution of values the estimates might take is centered around the true value of the parameter An estimator is unbiased if its average value (or expected value) is equal to the true value of the parameter Unbiased Estimators • • 4- Relative Frequency Distribution* (Figure ) 0 8 2 10 4 6 1 1 3 5 7 9 *Also called a probability density function (pdf) 4- Must determine if there is sufficient statistical evidence to indicate that Y is truly related to X (., b 0) Statistical Significance • Test for statistical significance using t-tests or p-values 4- First determine the level of significance Probability of finding a parameter estimate to be statistically different from zero when, in fact, it is zero Probability of a Type I Error 1 – level of significance = level of confidence Performing a t-Test 4- Performing a t-Test Use t-table to choose critical t-value with n – k degrees of freedom for the chosen level of significance n = number of observations k = number of parameters estimated • 4- Performing a t-Test If absolute value of t-ratio is greater than the critical t, the parameter estimate is statistically significant 4- Using p-Values Treat as statistically significant only those parameter estimates with p-values smaller than the maximum acceptable significance level p-value gives exact level of significance Also the probability of finding significance when none exists 4- Coefficient of Determination R2 measures the percentage of total variation in the dependent variable that is explained by the regression equation Ranges from 0 to 1 High R2 indicates Y and X are highly correlated 4- F-Test Used to test for significance of overall regression equation Compare F-statistic to critical F-value from F-table Two degrees of freedom, n – k & k – 1 Level of significance If F-statistic exceeds the critical F, the regression equation overall is statistically significant 4- Multiple Regression Uses more than one explanatory variable Coefficient for each explanatory variable measures the change in the dependent variable associated with a one-unit change in that explanatory variable 4- Use when curve fitting scatter plot Quadratic Regression Models • • • is U-shaped or U -shaped 4- Log-Linear Regression Models • • • • • 4-