Question

I need help plotting the question below in R

Plot a summary of the predictive distribution (i.e., predictive mean and 90% interval. You will find lines command very helpful.) for VIX returns ranging from-20% to 20%.

Answer 1

We solve this using the open source statistical package R , the R snippet is as below

# read the data into R dataframe
df<- read.csv("VIX.csv",header=TRUE)
str(df)

fit <- lm(cost~VIX,data=df)
summary(fit)

newdata = data.frame(VIX=15)

predict(fit, newdata, interval="predict")

# 1. Add predictions
pred.int <- predict(fit, interval = "prediction")
mydata <- cbind(df, pred.int)
# 2. Regression line + confidence intervals
library("ggplot2")
p <- ggplot(mydata, aes(VIX, SPX)) + geom_point() + stat_smooth(method = lm)
# 3. Add prediction intervals
p + geom_line(aes(y = lwr), color = "red", linetype = "dashed")+ geom_line(aes(y = upr), color = "red", linetype = "dashed")

The results are

> summary(fit)

Call:

lm(formula = SPX ~ VIX, data = df)

Residuals:

Min 1Q Median 3Q Max

-284.70 -88.06 -13.35 82.68 223.65

Coefficients:

Estimate Std. Error t value Pr(>|t|)   

(Intercept) 270.23 58.37 4.629 0.000208 ***

VIX 74.56 11.54 6.460 4.46e-06 ***

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 149.2 on 35 degrees of freedom

Multiple R-squared: 0.6986, Adjusted R-squared: 0.6819

F-statistic: 41.73 on 1 and 35 DF, p-value: 4.459e-06

> predict(fit, newdata, interval="predict")

fit lwr upr

1 1388.613 973.4366 1803.79