Question

a.Create a scatterplot for the data in the Length (in inches) and Braking Distance (in feet) columns. b.calculate the linear correlation between the data in the Length and Braking Distance columns. c) Explain the mathematical relationship between Length and Braking Distance based on the linear correlation coefficient. d) Create a scatterplot for the data in Displacement (in liters) and Highway MPG columns. E. calculate the linear correlation coefficient between the data in the Displacement and Highway MPG columns. f) Compare and contrast these two relationships: Length and Braking Distance Displacement and Highway MPG How are they similar? How are they different?

7 DISPLACEM 8 CITY 25 10 GHG HIGHWAY 4 LENGTH 5 BRAKING 6 CYLINDERS 3 WEIGHT 2 SIZE 1 CAR Row 6.6 34 1.6 133 4 2560 154 Small Chev Aveo 1 6.3 36 25 1.8 136 177 Honda Civic Mitsubishi Lancer 2740 Small 7.7 28 22 2.0 126 177 3610 Small 6.4 40 29 2.0 137 179 3225 Small VW Jetta 4 6.6 33 25 2.0 138 177 2895 Small Hyundai Elantra 35 6.1 27 1.6 132 167 2615 Small Kia Rio 6 8.3 26 2.5 20 180 135 3110 Subaru Impreza Ford Fusion Small 7 8.0 28 20 2.3 136 191 3320 Midsize CO 7.1 31 23 2.5 136 190 3215 Nissan Altima Midsize 8.3 26 19 3.5 128 191 3555 Midsize Nissan Maxima 10 7.7 30 21 24 140 4 194 3270 3465 Midsize Honda Accord 11 8.0 28 19 2.5 140 180 Volvo $60 VW Passat Midsize 12 8.0 29 19 20 4 135 188 189 3465 Midsize 13 7.3 21 31 24 137 4 3530 Toyota Camry Toyota Avalon Hyundai Azera Cadillac DTS Midsize 8.0 28 19 .5 139 6 197 3600 Large Large Large Large Large Large 8.7 26 3.3 18 134 193 3835 10.2 23 4.6 15 145 208 4085 96 24 16 4.6 143 215 4415 Lincoln Town 8.7 26 2.7 18 131 200 4170 Dodge Charger Merc Gr Marq 9.6 24 4.6 16 140 212 203 4180 20 10.2 25 4.6 17 143 4095 Large Buick Lucerne 21 7338 416789

Answer 1

Since the mode of calculation has not been mentioned, I have used R to create scatterplots and calculate the correlation coefficient as well. I am including the R code for each part as well.

a) Here I have taken Length in the x axis and Breaking distance in the y axis:

The rcode for this part is :

length<-c(154,177,177,179,177,167,180,191,190,191,194,180,188,189,197,193,208,215,200,212,203)
Breaking_dist<-c(133,136,126,137,138,132,135,136,136,128,140,140,135,137,139,134,145,143,131,140,143)

plot(length,Breaking_dist,xlab="Length(in inches)", ylab="Breaking Distance(in feet)", main="Scatterplot")

Scatterplot 160 170 180 190 200 210 Length(in inches) C Breaking Distance(in feet) 0

b) R code : cor(length,Breaking_dist)

The correlaion coefficient between length and breaking distance turns out to be 0.5375

c) Based on the correlation coefficient, there is a moderately strong positive correlation between length and breaking distance as the coefficient is slightly greater than 0.5

d) R code for scatter plot:

Displacement<-c(1.6,1.8,2.0,2.0,2.0,1.6,2.5,2.3,2.5,3.5,2.4,2.5,2.0,2.4,3.5,3.3,4.6,4.6,2.7,4.6,4.6)
HighwayMPG<-c(34,36,28,40,33,35,26,28,31,26,30,28,29,31,28,26,23,24,26,24,25)

plot(Displacement,HighwayMPG, xlab="Displacement(in litres)", ylab="Highway MPG",main="Scatterplot2")

Scatterplot2 4.5 2.0 1.5 2.5 3.0 3.5 4.0 Displacement(in litres) O OO O O Ot Highway MPG

e) R code : cor(Displacement,HighwayMPG)

The linear correlation coefficient for Displacement and highway MPG is -0.7737

f) Since the correlation is greater than 0.5 hence like the Length and breaking distance, this is also a strong correlation but since the sign is negative, it means that correlation is strongly negative that is when Displacement increases, Highway MPG decreases or visa versa unlike Length and Breaking distance where both increase/decrease together.