Please answer in detail Section 2. Variables and descriptive statistics. Describ
ID: 3224367 • Letter: P
Question
Please answer in detail
Section 2. Variables and descriptive statistics. Describe the variables used in your analysis. The data set contains nominal prices and nominal disposable income, which are unadjusted for inflation. One way to adjust for the effects of inflation is to convert nominal prices (income) into real prices (income) by dividing the nominal price (income) by the consumer price index (CPI) for that year as a number. In so doing, the values are on a “constant ruler,” namely in constant 1982-1984 dollars and cents. Constructs two graphs and describe in words the dynamics of real prices and real per capita income in the US during 1970-2016. [Attach the two graphs (one for the three prices and one for income) as Appendices 2 and 3, one page each.] Provide descriptive statistics for each variable in the data set. Make comments and interpretations based on these descriptive statistics.
Section 3.Estimation. Use OLS to estimate the linear and power forms of the demand function for beef:
Specification A : Qbeef = a+b1Pbeef+b2Ppork+b3Pchicken+b4I+b5T
Specification B: lnQbeef = a+b1lnPbeef+b2lnPpork+b3lnPchicken+b4lnI+b5T
where beefQ is per capita consumption of beef (pounds); beefP is real retail price of beef (cents per lb. on a retail weight basis); porkP is real retail price of pork (cents per lb. on a retail weight basis); chickenP is real retail price of chicken (cents per lb. on a retail weight basis); I is real per capita disposable personal income (dollars); T is the year dummy (=1 for 1970, 2 for 1971, 3 for 1973, etc.). [Attach the two Excel computer printouts as Appendices 4 and 5, one page each.]
Year Per capita consumption (pounds) Per capita consumption (pounds) Per capita consumption (pounds) Nominal retail price (cents per lb. on a retail weight basis) Nominal retail price (cents per lb. on a retail weight basis) Nominal retail price (cents per lb. on a retail weight basis) Annual, seasonally adjusted per capita nominal disposable income (dollars) Annual, seasonally adjusted CPI-U (index, 1982-84 = 100) Beef Pork Broilers Beef Pork Broilers 1970 84.6 55.8 36.6 99.9 77.4 40.8 3713 38.842 1971 83.9 60.5 36.5 106.2 69.8 41.1 3998 40.483 1972 85.3 54.7 38.1 116.6 82.7 41.4 4287 41.808 1973 80.5 48.7 36.7 139.7 109.2 59.6 4747 44.425 1974 85.6 52.7 36.6 143.8 107.8 56.0 5134 49.317 1975 88.2 42.9 36.3 152.2 134.6 63.3 5645 53.825 1976 94.3 45.5 39.4 145.7 134.0 59.7 6079 56.933 1977 91.8 47.0 40.2 145.8 125.4 60.1 6612 60.617 1978 87.3 47.0 42.5 178.8 143.6 66.5 7321 65.242 1979 78.1 53.3 46.0 222.4 152.5 67.7 8037 72.583 1980 76.6 57.3 45.8 233.6 147.5 70.9 8860 82.383 1981 77.3 54.7 46.9 234.7 161.2 73.2 9785 90.933 1982 77.0 49.1 47.0 238.4 185.6 71.4 10441 96.533 1983 78.6 51.8 47.4 234.1 179.7 72.5 11169 99.583 1984 78.4 51.5 49.2 235.5 171.4 81.0 12283 103.933 1985 79.2 51.9 51.0 228.6 171.4 76.3 12991 107.600 1986 78.8 49.0 52.0 226.8 188.8 83.5 13660 109.692 1987 73.9 49.2 55.1 238.4 199.4 78.5 14273 113.617 1988 72.6 52.5 55.3 250.3 194.0 85.4 15385 118.275 1989 69.0 52.0 56.6 265.7 193.5 92.7 16379 123.942 1990 67.7 49.7 59.5 281.0 224.9 89.9 17234 130.658 1991 66.6 50.2 61.9 288.3 224.2 88.0 17688 136.167 1992 66.1 52.7 65.5 284.6 209.5 86.9 18683 140.308 1993 64.6 51.9 67.9 293.4 209.1 89.0 19210 144.475 1994 66.3 52.5 68.8 282.9 209.5 90.1 19905 148.225 1995 66.6 51.7 67.9 284.4 206.1 91.7 20753 152.383 1996 67.1 48.3 69.2 280.2 233.7 97.3 21614 156.858 1997 65.7 47.8 71.4 279.5 245.0 100.2 22526 160.525 1998 66.7 51.5 72.0 277.1 242.7 104.4 23759 163.008 1999 67.5 52.6 76.3 287.8 241.5 105.6 24616 166.583 2000 67.8 51.2 77.0 306.4 258.2 107.1 26205 172.192 2001 66.3 50.4 76.8 337.7 269.4 110.5 27179 177.042 2002 67.8 51.6 80.7 331.5 265.7 107.4 28126 179.867 2003 65.0 51.9 81.8 374.6 265.8 103.4 29200 184.000 2004 66.2 51.5 84.5 406.5 279.2 107.0 30699 188.908 2005 65.6 50.1 86.0 409.1 282.7 105.6 31762 195.267 2006 65.9 49.5 86.7 397.0 280.8 104.9 33591 201.558 2007 65.3 50.8 85.3 415.8 287.1 111.5 34828 207.344 2008 62.5 49.5 83.5 432.5 293.7 120.7 36105 215.254 2009 61.1 50.2 79.8 426.0 292.0 128.1 35618 214.565 2010 59.6 47.8 82.4 439.5 311.4 126.3 36274 218.076 2011 57.3 45.7 82.9 482.7 343.4 129.1 37811 224.923 2012 57.3 45.9 80.4 498.6 346.7 133.5 39454 229.586 2013 56.3 46.8 81.8 528.9 364.4 149.0 39156 232.949 2014 54.1 46.4 83.3 597.1 402.0 153.0 40837 236.704 2015 53.9 49.7 88.9 628.9 385.3 148.0 42094 236.987 2016 estimated* 55.4 49.9 89.6 620.0 378.0 142.0 43431 240.009Explanation / Answer
The models are fitted using the R software:
> tt <- read.csv("clipboard",sep=" ")
> head(tt)
Qbeef Pbeef Pport Pchicken b4l b5T
1 84.6 99.9 77.4 40.8 3713 38.842
2 83.9 106.2 69.8 41.1 3998 40.483
3 85.3 116.6 82.7 41.4 4287 41.808
4 80.5 139.7 109.2 59.6 4747 44.425
5 85.6 143.8 107.8 56.0 5134 49.317
6 88.2 152.2 134.6 63.3 5645 53.825
> Qbeef_lm <- lm(Qbeef~.,tt)
> lnQbeef_lm <- lm(log(Qbeef)~log(Pbeef)+log(Pport)+log(Pchicken)+log(b4l)+log(b5T),tt)
> summary(Qbeef_lm)
Call:
lm(formula = Qbeef ~ ., data = tt)
Residuals:
Min 1Q Median 3Q Max
-6.9540 -1.9795 -0.3406 2.0696 7.6794
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.006e+02 3.321e+00 30.292 < 2e-16 ***
Pbeef -5.620e-02 1.909e-02 -2.944 0.00532 **
Pport 9.634e-02 4.959e-02 1.943 0.05891 .
Pchicken -9.433e-02 1.052e-01 -0.897 0.37492
b4l 1.224e-03 3.476e-04 3.523 0.00106 **
b5T -3.603e-01 6.815e-02 -5.288 4.43e-06 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 3.153 on 41 degrees of freedom
Multiple R-squared: 0.9172, Adjusted R-squared: 0.9071
F-statistic: 90.85 on 5 and 41 DF, p-value: < 2.2e-16
> summary(lnQbeef_lm)
Call:
lm(formula = log(Qbeef) ~ log(Pbeef) + log(Pport) + log(Pchicken) +
log(b4l) + log(b5T), data = tt)
Residuals:
Min 1Q Median 3Q Max
-0.09197 -0.03241 0.00544 0.03521 0.07669
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 6.12877 0.42477 14.429 < 2e-16 ***
log(Pbeef) -0.28864 0.07723 -3.737 0.000568 ***
log(Pport) 0.39781 0.13341 2.982 0.004804 **
log(Pchicken) -0.24171 0.14445 -1.673 0.101891
log(b4l) -0.14694 0.13373 -1.099 0.278268
log(b5T) 0.02848 0.17257 0.165 0.869749
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.04732 on 41 degrees of freedom
Multiple R-squared: 0.9043, Adjusted R-squared: 0.8927
F-statistic: 77.52 on 5 and 41 DF, p-value: < 2.2e-16
It can be conlcuded the regression model summaries that the log-transformations are not required here as the R2 decreases as well as the variables are not significant.