Topic_03_Elasticity_Estimation (1).pptm

# On the other hand if the regression explains none of

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On the other hand if the regression explains none of the variation in the dependent variable, then R 2 =0.

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Goodness of Fit and R 2 Statistics (a) R 2 = 0.98 (b) R 2 = 0.54 R 2 = 0.54 on the right panel shows that 46% of the variation in demand is due to random errors. 32
Do We Have the Right Functional Form? – Advertising and Demand (a) Linear (b) Quadratic Using a linear regression would be a mistake in this case. The actual relationship is more like a quadratic function. 33

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3.3 Statistical Significance of Estimated Coefficients How close the estimated coefficients are to their respective true values ? If the standard errors ( ) of the estimated values are low, then these values are good indicators of true values. An estimation method is unbiased if it produces estimated coefficients that are equal to true values on average. OLS is unbiased method. 34
Confidence Interval/Hypothesis Testing A manager may want to test if the price of rival product ( p r ) affects it demand ( y ). The estimated equation is: = + p r The estimated coefficients (and ) are less likely equal to their true values ( β 0 and β 1 ). In this case, we can construct a 95% (or any other) confidence interval such that the true value lies within this interval 95% of times. 35

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Hypothesis Testing The null hypothesis that rival’s coefficient is zero. Null hypothesis H 0 : = 0 Alternative H 1 : ≠ 0 If 95% confidence interval for includes zero can be tested by using t-statistic = ( - 0)/ . If the absolute value of t-statistics is > critical value (which is close to 2 for two-tailed 95% level), then we reject null hypothesis. 36
Hypothesis Testing That is, 95% confidence level (CI) does not include zero. There is 95% probability that rival’s price affects the product’s demand. Or simply that the explanatory variable is statistically significant (at 5% significant level or 95% confidence level) . 95% CI = ± t 95%, n-k-1 . If n= # of observations, k = # of explanatory variables, then n-k-1 = degree of freedom. 37

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3.4 Regression Specification It is important to correctly select the explanatory variables and distinguish correlation and causation . Correlation may NOT necessarily imply causation. For example, during the summer time incidence of both gasoline demand and sun burn are high, and so there is a strong correlation between them. Does that mean demand of gasoline causes sun burn? 38
Causation and Omitted Variables Obviously, NO ! There is a third factor in this case that is sunny days that is affecting both. Sometimes your analysis may omit some of the explanatory variables (not taken into consideration). In that case the resulting coefficient estimates may not be reliable. 39
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