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Unformatted text preview: FUNDAMENTALS OF FUNDAMENTALS MANAGERIAL MANAGERIAL ECONOMICS ECONOMICS 9th Edition By Mark Hirschey Statistical Analysis of Economic of Relations Relations Data Summary and Description l Measures of Central Tendency l Measures of Dispersion l Chapter 3 OVERVIEW Chapter 3 Hypothesis Testing l Economic Relations l Regression Analysis l Judging Regression Model Fit l Judging Variable Significance l l population parameters l sample statistics l mean mean l profit margin l median l mode l symmetrical l skewness l range l population variance l population standard deviation l sample variance l sample standard deviation l coefficient of variation l hypothesis test l Type I error l Type II error l z statistic statistic l t statistic l degrees of freedom l deterministic relation l statistical relation l dependent variable Chapter 3 KEY CONCEPTS l independent variable l time series l cross-section l linear model l multiplicative model l simple regression model l multiple regression model l standard error of the estimate l correlation coefficient l coefficient of determination l F statistic l Population Parameters l Data Summary and Description Description l Sample Statistics l Summary and descriptive measures. measures. l Characteristics of the entire universe. universe. Summary and descriptive measures. measures. l Characteristics of part of the entire universe. universe. l Basis for estimating population parameters. parameters. l Mean l l Measures of Central Tendency Tendency Average observation. Middle observation. Most common observation. l Median Mode l l l Comparing Measures of Central Tendency Tendency l Uniform population has similar measures. measures. l Nonuniform population has dissimilar measures. measures. Measures of Dispersion l Range l High versus low. l Variance and Standard Deviation l l Coefficient of Variation l Arithmetic mean of the squared deviation from the mean. from l Standard deviation is the square root of the variance. the Standard deviation divided by mean. l Risk/reward ratio. l Hypothesis Tests l Hypothesis Testing l Means Tests for Large Samples l Type I error: Incorrect rejection of true hypothesis. hypothesis. l Type II error: Incorrect failure to reject false hypothesis. false z statistic measures difference from statistic mean in standardized units in big mean samples. samples. t statistic measures difference from mean statistic in standardized units in small samples. in l Means Tests for Small Samples l l Deterministic and Statistical Relations Relations l Economic Relations Economic l Scatter Diagrams l Deterministic relation is true by definition, e.g., TR = PQ. definition, l Statistical relation exists if variables are related. variables Y-variable is dependent. l X-variables are independent. l Regression analysis is a powerful tool for the study of causal relations. tool l Regression Analysis l Linear and Multiplicative Models Linear (straight-line) relations imply unit-by-unit links. unit-by-unit l Multiplicative (curved-line) relations l Least Squares Method l imply nonlinear links. imply Best fitting line minimizes scatter about the regression line. about l Standard Error of the Estimate (SEE) SEE is the standard deviation of the dependent Y variable after controlling for all X variables. l SEE increases with scatter about the regression line. regression l SEE=0 if each data point is on the regression line. regression l l Judging Regression Model Fit Model l Confidence Intervals Y = Estimated Y ± 2 SEE with 95% Estimated SEE confidence. confidence. l Y = Estimated Y ± 3 SEE with 99% Estimated SEE confidence. confidence. l l Coefficient of Determination (R2) R2 = 100% means complete explanation. explanation. l R2 = 0% means no explanation. l r = 1 means perfect correlation. l r = 0 means no correlation. l Correlation Goodness of Fit l Corrected Coefficient of Determination l Adjusts R2 downward for small downward samples. samples. l Tells if R2 is statistically significant. F Statistic l t statistics l Judging Variable Judging Significance Significance l Interpreting t statistics Interpreting l t statistics compare a sample characteristic to the standard characteristic deviation of that characteristic. deviation A calculated t statistic more than two suggests a strong effect of X two on Y (95 % confidence). on l A calculated t statistic more than three suggests a very strong effect three of X on Y (99 % confidence). ...
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