## Regression Essay

Developing a linear regression model and estimate the effects of a tariffa)      To describe the data using diagrams and any statistics that seems appropriate.

The price mean and the standard deviation is 2.0461 and 0.4337 respectively, quantity mean and standard deviation is 495.2852 and 22.7671 respectively.

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The table below shows the results:Price:priceMean2.046062012Standard Error0.111975629Median1.95338747Standard Deviation0.

433679748Sample Variance0.188078123Quantity:quantityMean495.2852178Standard Error5.878442947Median500.8603165Standard Deviation22.

76711164Sample Variance518.3413722b)      To check if there is a trend in prices or the quantities demanded over the years?c)      (i) To compute 95% confidence intervals for prices and quantity demanded.  Having the price mean and the standard deviation as 2.0461 and 0.

4337, 95% confidence interval can be computed as;            Lower Interval = (-1.96*0.4337) + 2.0461 = 1.196            Upper interval = (1.96*0.

4337) + 2.0461 = 2.8962Thus 95% confidence interval for price is (1.

196, 2.8962).Having the quantity mean and standard deviation as 495.2852 and 22.7671, therefore 95% confidence interval can be computed as;            Lower interval = (-1.96*22.7671) + 495.

2852 = 450.6265            Upper interval = (1.96*22.7671) + 495.2852 = 539.9087Thus 95% confidence interval for quantity is (450.6265, 539.9087).

(ii) Confidence intervals show the interval in which the value of price or quantity can fall at, while simple mean just show a single value for the expected value of price or quantity.(d) Using linear regression, the inverse demand for Bananas can be estimated as;P = f’ (Q)       and Q = 594.96 – 48.522P Thus inverse demand function is P = 10.

76601 – 0.01761Q.(e) The regression equation and the adjusted R-squared.       Q = 594.

96 – 48.522P and adjusted R-squared is 0.8431.(f) Is demand for the year 2009 elastic or inelastic?  What did you expect for agricultural products?Using the formula  , where ?Q = -3.717, ?P = -0.222, P =1.448, and Q = 522.

478. Thus ed = (-3.717/-0.

222)*(1.448/522.478) = 16.7432 / 0.00277 = 6044.4765(g) Graph of demand function and supply function:From the chart the equilibrium price and quantity is approximately 2.

845217594 and 456.9043519 respectively. (h) To estimate the change in Producers’ and Consumers’ surplus from the imposition of the tariff that resulted in prices increasing from 1.448 to 1.7 euros per kilogram.Supply = P=-20+0.05QPrice = 1.4481.448 =-20+0.05QQ = 428.96Price = 1.71.7 =-20+0.05QQ = 434Demand = Q = 594.96 – 48.522PPrice = 1.448Q = 594.96 – 48.522(1.448)Q = 524.7001Price = 1.7Q = 512.4726Table summarizes the results:pricesupplydemand1.448428.96524.70011.7434512.4726The diagram below indicates the equilibrium and the changes in supply and demand due to the tarrif:Consumer surplus change = (price change X quantity change)/2Producer surplus change = (price change X quantity change)/ 2Consumer surplus = area AArea A = [2.845 X (594.96 – 456.90)] / 2Area A = 196.3992Producer surplus = area BArea B = [2.845 X (456.90-400)] / 2Area B = 80.95The following table summarizes the results;pricesupplydemand1.448428.96524.70011.7434512.4726equilibrium2.845217594456.9044456.904352at price zero0400594.96equilibrium consumer surplus196.399equilibrium producer surplus80.95change0.2525.04-12.2275producer surplus change1.27008consumer surplus change3.08133From the table producer surplus declines by 1.27008 whereas consumer surplus declines by 3.08133