Question

question 6 please

w The following random sample of vehicle weight and mileage hundreds of pounds) and Ymiles per gallon X (100 ) 20 Y( 234 a) Plot a scatter diagram of the data. Remember label your appropriately b) Based on a scatter diagram, would you estimate the correlation coefficient to be positive, close to ero, or negative? c) Explain your answer to part b.

Answer 1

Hi,

Using R software I have created the scatter plot. It can be easily plotted by hand as same as the below graph.

x <- c(20,26,35,29,39)
y <- c(23.4,22.0,16.1,18.8,15.7)
plot(x,y, pch = 16, cex = 1.0, col = "blue", main = "SCATTER PLOT", xlab = "Weight of Vehicle(in hundreds of pounds)", ylab = "Miles per gallon")
cor(x,y)

Just run this code in R you'll get,

> x <- c(20,26,35,29,39)
> y <- c(23.4,22.0,16.1,18.8,15.7)
> plot(x,y, pch = 16, cex = 1.0, col = "blue", main = "SCATTER PLOT", xlab = "Weight of Vehicle(in hundreds of pounds)", ylab = "Miles per gallon")

> cor(x,y)
[1] -0.970121

SCATTER PLOT 22 20 Miles per gallon 18 16 - 25 30 35 Weight of Vehicle(in hundreds of pounds)

Answers:

(a) The plot is given above.

(b) The thing we notice after observing the scatter diagram is that as the weight of a vehicle(in hundreds of pounds) increases the miles per gallon is decrease. Hence there is a negative correlation between the weight of a vehicle(in hundreds of pounds) and miles per gallon.

(c) As we can see that there is a deep fall of points as the weight of a vehicle(in hundreds of pounds) increases, hence we conclude that there is a strong negative correlation.

The value of correlation calculated above is -0.970121.