SD20020_Question 1
2022-11-01
Visualisation
library(car)## Loading required package: carDatascatterplot(price ~ sqft_living, data)
## [1] 0.7020437## [1] 0.4928654model <- lm(price ~ sqft_living, data)
model##
## Call:
## lm(formula = price ~ sqft_living, data = data)
##
## Coefficients:
## (Intercept) sqft_living
## -43867.6 280.8library(ggplot2)
ggplot(data, aes(sqft_living, price)) + geom_point() + stat_smooth(method = lm)## `geom_smooth()` using formula 'y ~ x'
summary(model)##
## Call:
## lm(formula = price ~ sqft_living, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1478255 -147564 -24169 106283 4360147
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -43867.602 4405.455 -9.958 <2e-16 ***
## sqft_living 280.807 1.938 144.924 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 261600 on 21611 degrees of freedom
## Multiple R-squared: 0.4929, Adjusted R-squared: 0.4928
## F-statistic: 2.1e+04 on 1 and 21611 DF, p-value: < 2.2e-16# Save the predicted values
yhat<- predict(model)
# Save the residual values
epsilon <- residuals(model)
cbind(yhat,epsilon)## yhat epsilon
## 1 287484.29 -6.558429e+04
## 2 677805.59 -1.398056e+05
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## 21612 405423.10 -5.423102e+03
## 21613 242555.22 8.244478e+04plot(cbind(yhat,epsilon))
abline(h = 0, lty = 2)
#Predicted with residual
cbind(data$sqft_living, epsilon)## epsilon
## 1 1180 -6.558429e+04
## 2 2570 -1.398056e+05
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## 2010 3110 -3.444412e+05
## 2011 1380 -7.164563e+04
## 2012 1290 -1.337303e+04
## 2013 1980 2.478704e+05
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## 2017 770 -1.635355e+04
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## 21613 1020 8.244478e+04plot(cbind(data$sqft_living, epsilon))
abline(h = 0, lty = 2)
#Autocorrelation
t<-c(1:200)
time<-cbind(t,epsilon)## Warning in cbind(t, epsilon): number of rows of result is not a multiple of
## vector length (arg 1)plot(time)
abline(h = 0, lty = 2)