Quiz #2 1. Suppose you are given the following simple dataset: X 2 8 9 13 Regress Y on X and you get: Y 5 9 12 18 Y = aˆ + bˆX 1) Which variable is the independent variable? Which one is the dependent variable? (5pts) 2) Calculate â and b̂ using the formulas below. Must show your work. (15pts) ( X i − X )(Yi − Y ) bˆ = ( X i − X )2 aˆ = Y − bˆX 2. Suppose demand for a product is determined by its price, consumers’ income, and the price of a related good. Use Q for demand, P for price, M for income, and PR for price of related good. The demand function is estimated using regression analysis. The results are reported below: SUMMARY OUTPUT 1 Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.744152135 0.553821042 0.459552605 530.2842631 80 Intercept P M PR Coefficients 125.56 -6.32 0.035 -9.89 Standard Error 15.87 4.17 t Stat P-value ??? 0.051 2.21 1) What is the R 2 of this regression? (5pts) 2) What is the degrees of freedom of this regression? (5pts) 3) What is the effect of a one-dollar increase in price (P) on demand (Q)? (5pts) 4) What is the effect of a one-dollar increase in income (M) on demand (Q)? (5pts) 5) What is the effect of a one-dollar increase in price of related good (PR) on demand (Q)? (5pts) 6) Calculate the t Stat (or t ratio marked with “???” in the table) for the coefficient on P? (5pts) 7) Test whether the effect of P on Q is significant at the 5% significance level using the t stat you just calculated. Show your work. (5pts) 8) Using the p-value 0.051 in the table, test if the effect of M on Q is significant at the 5% significance level. (5pts) 9) Using the values P=100, M=35,000, and PR=40, predict the demand (Q)? (5pts) 10) Using the value of predicted Q you just calculated for part 9), calculate the estimates of P The price elasticity of demand ( Eˆ = bˆ ). Show your work. (5pts) Q 2 The income elasticity of demand ( Eˆ M = cˆ M ). Show your work. (5pts) Q PR The cross-price elasticity of demand ( Eˆ XR = dˆ ). Show your work. (5pts) Q 3. Suppose the following is an estimated log-linear demand function: ln Q = 12 – 3.68 ln P – 0.59 ln M + 2.66 ln PR All parameter estimates are significant. 1) Is this good a normal or an inferior good? (5pts) 2) Is this good a complement of or substitute for the related good? (5pts) 3) What is the price elasticity of demand for this good? (5pts) 4) What is the income elasticity of demand for this good? (5pts) 3

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