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Problem 1. (50pts)
From microeconomic theory it is known that the demand for a commodity generally depends on the income of the consumer, the real price of the commodity, and the real price of complementary or competing products. Chicken.xls includes the per capita consumption of chicken (in pounds) in the United States for 1960-1982 along with disposable income per capita (in dollars) and the retail prices for chicken, pork, and beef (in cents).
A research firm specializing in agricultural economics has recruited you. Your first assignment is to assist one of the principals in the firm with a study for a chicken franchise on the price elasticities for various meat products.
(1.1) Plot chicken consumption vs. chicken price and calculate the correlation coefficient between these two variables. Describe the relationship. Does it make economic sense? Offer your explanation briefly. (10pts.)
As price increases consumption increases but this is correct as income increases as well. Eventually, consumption levels off, as the increasing wealth means people spend their money on other meats instead of chicken. The correlation coefficient =.794, which means this does have a positive linear correlation.
(1.2) Run a linear regression:
Chicken price vs. consumption
Chicken w/beef+pork+ beef
Chicken consumption over time increases
Chicken consumption=b0+b1*Income+b2*chicken price+b3*pork price+b4*beef price What’s the estimated regression equation? (5pts.)
(1.3) Identify significant and insignificant variables. Does the chicken consumption statistically depend on the beef and pork prices and the income? Give the statistical reason briefly (p-value). (5pts.)
Significant=chicken consumption(p< .05) income not stat significant. Pork price has p< .05 so they are also stat significant. Beef is greater than .05 and so is chicken price—they’re not significant. This means that these variables are not significant and do not play a role in consumption only pork prices do.
(1.4) How much variation in the chicken consumption is explained by the regression equation? (5pts.)
Variation seen by .9832—Good number for this type as variation typically should be ~75% or more
(1.5) Using the estimated regression equation, quantify how the chick consumption changes with the retail prices of chicken, pork and beef. Positively or negatively? Does it make economic sense? Offer your explanation briefly. (5pts.)
As the pork price increases by .11/Lb and beef price lowers by .02/Lb, chicken consumed is up .769. This doesn’t make sense. You expect lower beef price to increase consumption of beef and reduce consumption of chicken
An alternative is to consider an iso-elastic demand function: chicken consumption=A*[Income]a1[chicken price]a2[pork price]a3[beef price]a4
(1.6) Using a log-log transform, can you get a linear regression model? What’s the estimated regression equation? (Hint: taking the ln-transform of all variables) (5pts.)
Plotting residuals of ln transform:
This model is slightly better than standard regression
(1.7) Identify significant and insignificant variables (p-value). Does the chicken consumption statistically depend on the beef and pork prices and the income? Give the statistical reason briefly. (5pts.)
Chicken consumption, as well as ln transform of pork price is statistically significant..the chicken and beef prices are not. Again, beef and chicken prices do not have signficance, meaning they do not affect chicken consumption. Income is also not statistically signficant, which means that increase in income doesn’t mean less or more chicken is eaten....