13. You\'re hired by Farmer Vin, a famous producer of bacon and ham, to test the
ID: 3223502 • Letter: 1
Question
13. You're hired by Farmer Vin, a famous producer of bacon and ham, to test the possibility that feeding pigs at night allows them to grow faster than feeding them during the day. You take 200 pigs (from new- born piglets to extremely old porkers) and randomly assign them to feeding only during the day or feeding only at night and, after six months, end up with the following (admittedly very hypothetical) equation: Wii 12 3.5Gi 7.0D 0.25F (1.0) (1.0) (0.10) 2.5 7.0 3.5 R2 70 N 200 DW 0.50 where: W the percentage weight gain of the ith pig Gi a dummy variable equal to 1 if the ith pig is a male, 0 otherwise Di a dummy variable equal to 1 if the ith pig was fed only at night, 0 if only during the day Fi the amount of food (pounds) eaten per day by the ith pig a. Test for serial correlation at the 5-percent level in this equation. b. what econometric problems appear to exist in this equation? (Hint: Be sure to make and test appropriate hypotheses about the slope coefficients.) c. The goal of your experiment is to determine whether feeding at night represents a significant improvement over feeding during the day. What can you conclude?Explanation / Answer
a) As a rule of the thumb, a DW(d) value of less than 1 indicates serial correlation. However, we must perform a formal test as follows
Ho: No serial correlation
H1: Positive correlation
Decision rule is if d<DL, reject H0, while if d>DU, don't reject H0
Given d =.5 and n = sample size = 200 and k = no of predictor variables = 3
At a 95% level, DL = 1.738 and DU = 1.799
d = .5 is < 1.738 and we reject null.
b) For each of the slope coefficient, we can compute the p-value based on tstat
df = n-k-1 = 200-3-1= 196 and p-value is as follows
pg = .000576; pd = 0 and pf = .013
Since each p-value is less than .05, each of slope coefficient is significant. From part a, there is already
presence of correlation and hence we get a biased model
c) As we have established the presence of serial correlation and all the slopes are not zero, there is no way to determine whether feeding at night is an improvement.
d) Order of observations won't change any of the underlying statistic namely, mean/std err etc. Hence, answer to any of previous part won't change. We are randomly assigning whether each pig was fed at day or night. Only if this wasn't random, after ordering we would have 2 distinct group pairs namely piglets and day, old and night which would lead to incorrect results.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.