Question

5. The following questions refer to this regression equation, (standard errors in parentheses.) (points) + Q = 8,400 (1,732) 10 P + (2.29) 5A (1.36) 4 Px (1.75) + 0.051, (0.15) R2 = 0.65 N = 120 F = 35.25 Standard error of estimate = 34.3 Q = Quantity demanded P = Price = 1,000 A = Advertising expenditures, in thousands - 40 PX = price of competitor's good = 800 I = average monthly income = 4,000

Answer 1

a) The following formula is used to calculate the own-price elasticity. price elasticity =- % change in quantity demanded % change in price calculate the own-price elasticity of P.

calculate the own-price elasticity of P. % change in quantity demanded price elasticity => % change in price AQ P =D =-10x 1000 = coefficientofpx 8400-10(1000) + 5(40) + 4(800) +0.05(4000) 1000 8400-10000+ 200+3200+ 200 1000 = -10% 2000 =-5 Thus, own-price elasticity is -5. It means that price and quantity demanded have inverse relationship. With 1% increase (decreases) in price, quantity demanded decreases (increases) by 5%. ii) calculate the own-price elasticity of A.

price elasticity = % change in quantity demanded % change in price _ ΔΩ Α X- ΔΑ Ο 40 = coefficientofA - 8400-10(1000) + 5(40) +4(800) +0.05(4000) 40 = 5x 8400-10000+ 200+3200+ 200 40 *** 2000 = 0.1 Thus, price elasticity of advertising is 0.1. It means that adverting and quantity demanded have direct relationship. With 1% increase (decreases) in adverting, quantity demanded increases (decreases) by 0.1%. 111) calculate the cross-price elasticity between Q and Px.

% change in quantity demanded cross-price elasticity = = % change in price _AQ Py AP 800 = coefficientofP, X- 8400-10(1000) + 5(40) +4(800) +0.05(4000) 800 = 4x 8400-10000+ 200+3200 + 200 = 4x 800 2000 = 1.6 Thus, cross-price elasticity is 1.6. It means that price of good X and quantity demanded have direct relationship. With 1% increase (decreases) in price of good X, quantity demanded increases (decreases) by 1.6%. Both the goods are substitute in nature. iv) calculate the income elasticity.

... cross-price elasticity = % change in quantity demanded % change in price _AQ 1 ΔΙΟ 4000 = coefficientofi x- 8400-10(1000) + 5(40) +4(800) +0.05(4000) 4000 = 0.05% 8400-10000 + 200+3200 + 200 -0.054000 2000 = 0.1 Thus, income elasticity is 0.1. It means that the income and quantity have direct relationship. With 1% increase (decreases) in income, quantity demanded increases (decreases) by 0.1%. it means that goods are normal goods. b) find t-statistic of each variable. The following formula is used to calculate t-statistic.

t-statistics = coefficient standard error Find t-statistic of P, A, Px and I. For P, t-statistics = 10 = 14:37 For A, t-statistics - =13.68 1.36 For Px, t-statistics = 45 = 2.29 For I, t-statistics = 0.05 – 10.33 005 t-statistics = 0.15

Assume 95% as the level of significance If t- statistic is less than 2, it is not statistically significant. It means that P, A and Px are all statistically significant and I is not. c) R-squared is the proportion of variations in the dependent variable that is explained by the independent variables. The following formula is used to calculate the r squared. explained variation (explained sum of squares) R-squraed = expla Total variation(totalsumofsquare) It determines how well the model fits the dat. If it is 1, it is a perfect fit and if it is 0, the model is of poor choice. R-squared is 0.65 or 65%. It means that 65% of the variation in the dependent variable that is quantity demanded is explained by all the independent carriable that is own price, price of good X, advertising and income.

the quality of the model could be known by F-value, R-squared and t-statistic. Here, value of Fis 35.25 which is very high that implies that the repression equation is significant and also, sample size is also large. R-squared is 0.65 or 65%. It means that 65% of the variation in the dependent variable that is quantity demanded is explained by all the independent carriable that is own price, price of good X, advertising and income. One of the variables that is income is not statistically significant. Other are significant, it is not affecting OLS much. No major issue or concern is found. It is of good fit. Note: According to HOMEWORKLIB POLICY, only first four sub-parts must be attempted by an expert at a time. Please post other questions separately.