Statistics and Soft Drink
CASE 1 - DEMAND ESTIMATION and ELASTICITY: Soft Drinks in the U.S.
Demand can be estimated with experimental data, time-series data, or cross-section data. In this case, cross-section data appear in the Excel file. Soft drink consumption in cans per capita per year is related to six-pack price, income per capita, and mean temperature across the 48 contiguous states in the United States.
QUESTIONS
1. Given the data, please construct (a) a multiple linear regression equation and (b) a log-linear (exponential) regression equation for demand by MS Excel. (20%)
2. Given the MS Excel output in question 1, please compare the two regression equations’ coefficient of determination (R-square), F-test and t-test. Which equation is a good (better) fit? Which equation shows the stronger overall significance to predict the future demand? Which equation will you choose for a better demand estimation? Explain your answer in the language of statistics. (20%)
3. Given your choice of equation in question 2, please interpret each coefficient of independent variable in the soft drink demand estimated equation. (10%)
4. Given your choice of equation in question 2, how many cans/capita/year on soft drink should be for a state in which 6-pack price=$2.45, Income/Capita=$36,500, and Mean Temp= 68°F? (20%)
5. Given your choice of equation in question 2 and the numbers in question 4, please calculate the price elasticity of demand and income elasticity. Comment on whether the demand is elastic or inelastic and whether soft drink is necessity, normal good or luxury good. (10%)
6. Now omit the price and temperature from the regression equation then run the regression again. Given the Excel output of only one independent variable, income, should a marketing plan for soft drinks be designed that relocates most canned drink machines into low-income neighborhoods? Please explain your answer in the language of economics.
Demand can be estimated with experimental data, time-series data, or cross-section data. In this case, cross-section data appear in the Excel file. Soft drink consumption in cans per capita per year is related to six-pack price, income per capita, and mean temperature across the 48 contiguous states in the United States.
QUESTIONS
1. Given the data, please construct (a) a multiple linear regression equation and (b) a log-linear (exponential) regression equation for demand by MS Excel. (20%)
2. Given the MS Excel output in question 1, please compare the two regression equations’ coefficient of determination (R-square), F-test and t-test. Which equation is a good (better) fit? Which equation shows the stronger overall significance to predict the future demand? Which equation will you choose for a better demand estimation? Explain your answer in the language of statistics. (20%)
3. Given your choice of equation in question 2, please interpret each coefficient of independent variable in the soft drink demand estimated equation. (10%)
4. Given your choice of equation in question 2, how many cans/capita/year on soft drink should be for a state in which 6-pack price=$2.45, Income/Capita=$36,500, and Mean Temp= 68°F? (20%)
5. Given your choice of equation in question 2 and the numbers in question 4, please calculate the price elasticity of demand and income elasticity. Comment on whether the demand is elastic or inelastic and whether soft drink is necessity, normal good or luxury good. (10%)
6. Now omit the price and temperature from the regression equation then run the regression again. Given the Excel output of only one independent variable, income, should a marketing plan for soft drinks be designed that relocates most canned drink machines into low-income neighborhoods? Please explain your answer in the language of economics.