An article reports data on X= distance between a cyclist and the roadway center

Question

An article reports data on X= distance between a cyclist and the roadway center line and Y= the separation between the cyclist and a passing car. from ten streets with bike lanes. The paired distances (Xi, Yi) are determined by photography and are given below in feet.

x= 12.8, 12.9, 12.9, 13.6, 14.5, 14.6, 15.1, 17.5, 19.5, 20.8

y= 5.5, 6.2, 6.3, 7.0, 7.8, 8.3, 7.1, 10.0, 10.8, 11.0

(a). Compute Sx,y, S2x, S2y, and rx,y.

(b). Indicate how the quantities in part (a) would change if the ditsances had been given in inches.

Explanation / Answer

a)we can get the results easily with these R codes

x=c(12.8, 12.9, 12.9, 13.6, 14.5, 14.6, 15.1, 17.5, 19.5, 20.8)
y=c(5.5, 6.2, 6.3, 7.0, 7.8, 8.3, 7.1, 10.0, 10.8, 11.0)
cor(x,y)
var(x)
var(y)
cov(x,y)

Now Sx,y=Cov(x,y)= 5.46

S2x=var(x)= 8.268444

S2y=var(y)=3.906667

rx,y=cor(x,y)= 0.9606774

b)If the distances are given in inches each quantity will be multiplied by 12 in x and y

Now rx,y will remain same but var(x),var(y),cov(x,y) will be multiplied by 12**2=144

i.e

Now Sx,y=Cov(x,y)= 5.46

S2x=var(x)= 1190.656

S2y=var(y)=562.56

rx,y=cor(x,y)= 0.9606774

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