Greene. Econometric Analysis, 8ed.

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Chapter 3. Least Squares Regression

Table 3.1

Load libraries

library(AER)
library(stargazer)
library(knitr)
library(kableExtra)

Data Matrices

df <- as.data.frame(read.csv("data/TableF3-1.csv", fileEncoding="UTF-8-BOM", header=TRUE))
df1 <- df[, c(8, 7, 2, 5, 6)]
# df1$Constant=1 #To add a column populated with a constant 
kable(df1) %>%
  kable_styling(full_width = F) 

RealInv	Trend	RealGNP	Interest	Infl
2.484	1	87.1	9.23	3.4
2.311	2	88.0	6.91	1.6
2.265	3	89.5	4.67	2.4
2.339	4	92.0	4.12	1.9
2.556	5	95.5	4.34	3.3
2.750	6	98.7	6.19	3.4
2.828	7	101.4	7.96	2.5
2.717	8	103.2	8.05	4.1
2.445	9	102.9	5.09	0.1
1.878	10	100.0	3.25	2.7
2.076	11	102.5	3.25	1.5
2.168	12	104.2	3.25	3.0
2.356	13	105.6	3.25	1.7
2.482	14	109.0	3.25	1.5
2.637	15	111.6	3.25	0.8

Application 3.2 pp.30-32

coef(pp32a <- lm(RealInv ~ Trend + RealGNP + 1, data = df))

## (Intercept)       Trend     RealGNP 
##  -6.8555213  -0.1800237   0.1077841

coef(pp32b <- lm(RealInv ~ Trend + 1, data = df))

##  (Intercept)        Trend 
##  2.468009524 -0.006067857

Example 3.1

Partial Correlations, (& Table 3.2)

col2 <- lm(RealInv ~ Trend + RealGNP + Interest + Infl + 1, data = df)
coef(col2)

## (Intercept)       Trend     RealGNP    Interest        Infl 
## -6.21967209 -0.16088526  0.09908417  0.02017157 -0.01165919

col4 <- cor(df1)[1,-1]
col4

##      Trend    RealGNP   Interest       Infl 
## -0.1036346  0.1487904  0.5530208  0.1919226

pcor <- solve(cor(df1))
dcor <- 1/sqrt(diag(pcor))
col5 <- (-pcor * (dcor %o% dcor))[1,-1]
col5

##       Trend     RealGNP    Interest        Infl 
## -0.73284302  0.79226230  0.18602513 -0.09231543

Example 3.2

Fit of a Consumption Function

df <- as.data.frame(read.csv("data/TableF2-1.csv", fileEncoding="UTF-8-BOM", header=TRUE))
c(mean(df$X), mean(df$C))

## [1] 323.2727 273.2727

summary.aov(ols1 <- lm(C ~ X, data = df))

##             Df Sum Sq Mean Sq F value Pr(>F)  
## X            1   5768    5768   7.579 0.0224 *
## Residuals    9   6850     761                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

ols2 <- lm(C ~ X, data = subset(df, df$W == 0))
ols3 <- lm(C ~ X + W, data = df)
stargazer(ols1, ols2, ols3, keep.stat=c("rsq"), no.space=TRUE, type="text")

## 
## ======================================
##               Dependent variable:     
##          -----------------------------
##                        C              
##             (1)      (2)       (3)    
## --------------------------------------
## X         0.685**  0.853***  0.858*** 
##           (0.249)  (0.099)   (0.085)  
## W                           -50.690***
##                              (5.932)  
## Constant  51.895    15.907    14.495  
##          (80.844)  (31.643)  (27.299) 
## --------------------------------------
## R2         0.457    0.937     0.946   
## ======================================
## Note:      *p<0.1; **p<0.05; ***p<0.01

Example 3.3

Analysis of Variance Table (& Table 3.4.)

df <- as.data.frame(read.csv("data/TableF3-1.csv", fileEncoding="UTF-8-BOM", header=TRUE))
summary(mols  <- lm(RealInv ~ Trend + RealGNP + Interest + Infl, data = df))$r.squared

## [1] 0.7878083

deviance(mols)

## [1] 0.2036798

summary.aov(sols <- lm(RealInv ~ 1, data = df))

##             Df Sum Sq Mean Sq F value Pr(>F)
## Residuals   14 0.9599 0.06856

anova(sols, mols)

## Analysis of Variance Table
## 
## Model 1: RealInv ~ 1
## Model 2: RealInv ~ Trend + RealGNP + Interest + Infl
##   Res.Df     RSS Df Sum of Sq      F   Pr(>F)   
## 1     14 0.95989                                
## 2     10 0.20368  4   0.75621 9.2818 0.002125 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1