`Investment.Rd`

US data for fitting an investment equation.

`data(Investment)`

An annual time series from 1963 to 1982 with 7 variables.

- GNP
nominal gross national product (in billion USD),

- Investment
nominal gross private domestic investment (in billion USD),

- Price
price index, implicit price deflator for GNP,

- Interest
interest rate, average yearly discount rate charged by the New York Federal Reserve Bank,

- RealGNP
real GNP (= GNP/Price),

- RealInv
real investment (= Investment/Price),

- RealInt
approximation to the real interest rate (= Interest - 100 * diff(Price)/Price).

Table 15.1 in Greene (1993)

Greene W.H. (1993). *Econometric Analysis*, 2nd edition.
Macmillan Publishing Company, New York.

Executive Office of the President (1984). *Economic Report of the
President*. US Government Printing Office, Washington, DC.

```
## Willam H. Greene, Econometric Analysis, 2nd Ed.
## Chapter 15
## load data set, p. 411, Table 15.1
data(Investment)
## fit linear model, p. 412, Table 15.2
fm <- lm(RealInv ~ RealGNP + RealInt, data = Investment)
summary(fm)
#>
#> Call:
#> lm(formula = RealInv ~ RealGNP + RealInt, data = Investment)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -34.987 -6.638 0.180 10.408 26.288
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) -12.53360 24.91527 -0.503 0.622
#> RealGNP 0.16914 0.02057 8.224 3.87e-07 ***
#> RealInt -1.00144 2.36875 -0.423 0.678
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Residual standard error: 17.21 on 16 degrees of freedom
#> (1 observation deleted due to missingness)
#> Multiple R-squared: 0.8141, Adjusted R-squared: 0.7908
#> F-statistic: 35.03 on 2 and 16 DF, p-value: 1.429e-06
#>
## visualize residuals, p. 412, Figure 15.1
plot(ts(residuals(fm), start = 1964),
type = "b", pch = 19, ylim = c(-35, 35), ylab = "Residuals")
sigma <- sqrt(sum(residuals(fm)^2)/fm$df.residual) ## maybe used df = 26 instead of 16 ??
abline(h = c(-2, 0, 2) * sigma, lty = 2)
if(require(lmtest)) {
## Newey-West covariances, Example 15.3
coeftest(fm, vcov = NeweyWest(fm, lag = 4))
## Note, that the following is equivalent:
coeftest(fm, vcov = kernHAC(fm, kernel = "Bartlett", bw = 5, prewhite = FALSE, adjust = FALSE))
## Durbin-Watson test, p. 424, Example 15.4
dwtest(fm)
## Breusch-Godfrey test, p. 427, Example 15.6
bgtest(fm, order = 4)
}
#> Loading required package: lmtest
#> Loading required package: zoo
#>
#> Attaching package: ‘zoo’
#> The following objects are masked from ‘package:base’:
#>
#> as.Date, as.Date.numeric
#>
#> Breusch-Godfrey test for serial correlation of order up to 4
#>
#> data: fm
#> LM test = 12.07, df = 4, p-value = 0.01684
#>
## visualize fitted series
plot(Investment[, "RealInv"], type = "b", pch = 19, ylab = "Real investment")
lines(ts(fitted(fm), start = 1964), col = 4)
## 3-d visualization of fitted model
if(require(scatterplot3d)) {
s3d <- scatterplot3d(Investment[,c(5,7,6)],
type = "b", angle = 65, scale.y = 1, pch = 16)
s3d$plane3d(fm, lty.box = "solid", col = 4)
}
#> Loading required package: scatterplot3d
```