I will first set up my working directory.
used (Mb) gc trigger (Mb) limit (Mb) max used (Mb)
Ncells 597269 31.9 1356358 72.5 NA 700248 37.4
Vcells 1099361 8.4 8388608 64.0 49152 1963372 15.0cat("\f") # Clear the console# Set working directory and path to data
setwd("/Users/arvindsharma/Dropbox/WCAS/Econometrics/")plot(x = diamond$carat,
y = diamond$price,
xlab = "Mass (carats)",
ylab = "Price (Singapore $)",
main = "Price of Diamonds By Weight",
sub = "",
bg = "lightblue", # a vector of background colors (Graphical Parameters)
col = "black", # the colors for lines and points (Graphical Parameters)
cex = 1.1, # a numerical vector giving the amount by which plotting characters and symbols should be scaled relative to the default = 1 (Graphical Parameters)
pch = 21, # a vector of plotting characters or symbols (Graphical Parameters) {triangle, empty circle, filled circle, square,...}
frame = FALSE # frame.plot - a logical indicating whether a box should be drawn around the plot.
)
?abline
abline(reg = lm(data = diamond,
price ~ carat,
),
lwd = 2, # line width, default = 1
col = "blue"
)
We estimate an expected 3721.02 (SIN) dollar increase in price for every carat increase in mass of diamond.
The intercept -259.63 is the expected price of a 0 carat diamond.
(Intercept) I(carat - mean(carat))
500.0833 3721.0249 Thus $500.1 is the expected price for the average sized diamond of the data (0.2042 carats).
### PREDICTED VALUES SPECIFIC VALUES
new_x <- c(0.16,
0.27,
0.34
)
coef(fit)[1] + coef(fit)[2] * new_x[1] 335.7381 745.0508 1005.5225## USE THE PREDICT FUNCTION
?predict
predict(object = fit,
newdata = data.frame(carat = new_x)
) 1 2 3
335.7381 745.0508 1005.5225 ### PREDICTED VALUES FOR THE ENTIRE DATA
predict(object = fit,
data = data.frame(carat = new_x)
) 1 2 3 4 5 6 7 8
372.9483 335.7381 372.9483 410.1586 670.6303 335.7381 298.5278 447.3688
9 10 11 12 13 14 15 16
521.7893 298.5278 410.1586 782.2611 335.7381 484.5791 596.2098 819.4713
17 18 19 20 21 22 23 24
186.8971 707.8406 670.6303 745.0508 410.1586 335.7381 372.9483 335.7381
25 26 27 28 29 30 31 32
372.9483 410.1586 372.9483 410.1586 372.9483 298.5278 372.9483 931.1020
33 34 35 36 37 38 39 40
931.1020 298.5278 335.7381 335.7381 596.2098 596.2098 372.9483 968.3123
41 42 43 44 45 46 47 48
670.6303 1042.7328 410.1586 670.6303 670.6303 298.5278 707.8406 298.5278 y <- diamond$price; x <- diamond$carat; n <- length(y)
fit <- lm(formula = y ~ x)
# equivalent
fit <- lm(data=diamond,
formula = price ~ carat
)
e <- resid(fit)
plot(x = diamond$carat,
y = resid(lm(y~x)),
xlab = "Mass (carats)",
ylab = "Residuals (SIN $) ",
main = "Residual vs X",
sub = "price ~ carat"
); abline(h = 0,
col = "blue",
lwd = 2) # y values for horizontal lines
?abline
yhat <- predict(fit)
max( abs( e - ( y - yhat ) ) ) # y = diamond$price ; yhat = predicted (diamond$price)[1] 5.57776e-13[1] 5.57776e-13x <- runif(100,-3,3) ; y <- x + sin(x) + rnorm(100,sd=.2);
plot(x = x,
y = y,
xlab = "Real Number Line (Domain)",
ylab = "Y axis (Range)",
main = "Raw Data",
col = 'red',
cex = .8,
pch = 16);abline(reg = lm(y~x),
col = "blue",
lwd = 2)
plot(x = x,
y = resid(lm(y ~ x)),
main = "Residuals vs Domain (Real Number Line)",
xlab = "Real Number Line (Domain)",
ylab = "Residuals: lm(y ~ x) ",
col = "red",
cex = .8,
pch = 16) ; abline(h = 0,
col = "blue",
lwd = 2)
# Construct data
x <- runif(n = 100,
min = 0,
max = 6);y <- x + rnorm(n = 100,
mean = 0,
sd = .001 * x
)
# PLot raw data
plot(x = x,
y = y,
xlab = "Real Number Line (Domain)",
ylab = "Y axis (Range)",
main = "Raw Data",);abline(reg = lm(y~x))
