OOhannessian_Assignment11

head(cars)

##   speed dist
## 1     4    2
## 2     4   10
## 3     7    4
## 4     7   22
## 5     8   16
## 6     9   10

plot(cars, xlab = "Speed in mph", ylab = "Stopping Distance in ft", las = 1)
lines(lowess(cars$speed, cars$dist, f = 2/3, iter = 3), col = "red")
title(main = "Cars")

plot(cars, xlab = "Speed in mph", ylab = "Stopping Distance in ft", las = 1, log = "xy")
title(main = "Cars (logarithmic scales)")
lines(lowess(cars$speed, cars$dist, f = 2/3, iter = 3), col = "red")

Speed <- log(cars$speed)
Stopping_Distance <- log(cars$dist)
lregression <- lm(Stopping_Distance ~ Speed, data = cars)
summary(lregression)

## 
## Call:
## lm(formula = Stopping_Distance ~ Speed, data = cars)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.00215 -0.24578 -0.02898  0.20717  0.88289 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  -0.7297     0.3758  -1.941   0.0581 .  
## Speed         1.6024     0.1395  11.484 2.26e-15 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4053 on 48 degrees of freedom
## Multiple R-squared:  0.7331, Adjusted R-squared:  0.7276 
## F-statistic: 131.9 on 1 and 48 DF,  p-value: 2.259e-15

par(mfrow = c(2, 2))
plot(lregression)

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• The R-squared value is 73.31% (high) and looks good.

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