Greene. Econometric Analysis, 8ed.
Solomon Negash
April 22, 2020
Chapter 2. The Linear Regression Model
Example 2.1
Load libraries
library(AER)
library(stargazer)Keynes’s Consumption Function (pp.13)
df <- as.data.frame(read.csv("data/TableF2-1.csv", fileEncoding="UTF-8-BOM", header=TRUE))
plot(C ~ X, col="blue", main="FIGURE 2.1 Consumption Data, 1940-1950.", pch = 19,
xlim = c(235, 375), ylim = c(225, 350), data = df)
summary(fm <- lm(C ~ X, data=df))##
## Call:
## lm(formula = C ~ X, data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -35.347 -26.440 9.068 20.000 31.642
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 51.8951 80.8440 0.642 0.5369
## X 0.6848 0.2488 2.753 0.0224 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 27.59 on 9 degrees of freedom
## Multiple R-squared: 0.4571, Adjusted R-squared: 0.3968
## F-statistic: 7.579 on 1 and 9 DF, p-value: 0.02237abline(fm, col="red")
summary(fm2 <- lm(C ~ X, data=subset(df, df$W==1)))##
## Call:
## lm(formula = C ~ X, data = subset(df, df$W == 1))
##
## Residuals:
## 3 4 5 6
## -0.4671 -2.2905 -6.0845 8.8420
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -78.8388 131.2014 -0.601 0.609
## X 0.9853 0.3929 2.507 0.129
##
## Residual standard error: 7.767 on 2 degrees of freedom
## Multiple R-squared: 0.7587, Adjusted R-squared: 0.638
## F-statistic: 6.287 on 1 and 2 DF, p-value: 0.129abline(fm2, col="orange")
summary(fm3 <- lm(C ~ X, data=subset(df, df$W==0)))##
## Call:
## lm(formula = C ~ X, data = subset(df, df$W == 0))
##
## Residuals:
## 1 2 7 8 9 10 11
## 4.50494 -14.76444 -4.12361 11.11312 -0.09504 10.75802 -7.39299
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 15.90735 31.64252 0.503 0.636516
## X 0.85306 0.09894 8.622 0.000347 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 10.48 on 5 degrees of freedom
## Multiple R-squared: 0.937, Adjusted R-squared: 0.9244
## F-statistic: 74.33 on 1 and 5 DF, p-value: 0.0003465abline(fm3, col="orange")
text(C ~ X, data = df, labels=YEAR, pch = 19, cex = .9, pos = 3, font=3)
Example 2.2.
Earnings and Education
PSID76 <- as.data.frame(read.csv("data/TableF5-1.csv", fileEncoding="UTF-8-BOM", header=TRUE))
df <- subset(PSID76, PSID76$LFP==1)
earning <- log(df$WHRS*df$WW)
onevar <- lm(earning ~ WE, data = df)
twovar <- lm(earning ~ WE + WA, data = df)
threevar <- lm(earning ~ WE + WA + I(WA^2), data = df)
stargazer(onevar, twovar, threevar, no.space=TRUE, type="text")##
## ======================================================================================
## Dependent variable:
## ------------------------------------------------------------------
## earning
## (1) (2) (3)
## --------------------------------------------------------------------------------------
## WE 0.064** 0.066*** 0.067***
## (0.025) (0.025) (0.025)
## WA 0.013* 0.158*
## (0.008) (0.082)
## I(WA2) -0.002*
## (0.001)
## Constant 7.252*** 6.692*** 3.672**
## (0.328) (0.467) (1.768)
## --------------------------------------------------------------------------------------
## Observations 428 428 428
## R2 0.014 0.021 0.028
## Adjusted R2 0.012 0.016 0.021
## Residual Std. Error 1.203 (df = 426) 1.200 (df = 425) 1.197 (df = 424)
## F Statistic 6.239** (df = 1; 426) 4.550** (df = 2; 425) 4.094*** (df = 3; 424)
## ======================================================================================
## Note: *p<0.1; **p<0.05; ***p<0.01Example 2.3
The U.S. Gasoline Market
df <- as.data.frame(read.csv("data/TableF2-2.csv", fileEncoding="UTF-8-BOM", header=TRUE))
lnGPP <- log(df$GASEXP/(df$POP * df$GASP))
summary(lm(lnGPP ~ log(INCOME) + log(GASP) + log(PNC) + log(PUC) + 1, data=df))##
## Call:
## lm(formula = lnGPP ~ log(INCOME) + log(GASP) + log(PNC) + log(PUC) +
## 1, data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.13831 -0.02835 0.01303 0.03372 0.07431
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -21.21109 0.75322 -28.160 <2e-16 ***
## log(INCOME) 1.09587 0.07771 14.102 <2e-16 ***
## log(GASP) -0.02121 0.04377 -0.485 0.6303
## log(PNC) -0.37361 0.15707 -2.379 0.0215 *
## log(PUC) 0.02003 0.10330 0.194 0.8471
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.05071 on 47 degrees of freedom
## Multiple R-squared: 0.9584, Adjusted R-squared: 0.9549
## F-statistic: 271 on 4 and 47 DF, p-value: < 2.2e-16Example 2.7
Nonzero Conditional Mean of the Disturbances
set.seed(123)
x <- abs(rnorm(1000))
eps <- rnorm(x, mean =0, sd = 1.0)
y <- 25 + 5*x +5*(x^2) + eps
fm<-lm(y~x)
plot(x,y, pch=16, cex = .4, main = "FIGURE 2.2")
abline(fm, col="red")