Question

15. Engineers for a car manufacturer wanted to analyze the relationship between the speed x of their new model (The Bullet) and its gas mileage y for regular unleaded gasoline. The car was test driven at different speeds in the laboratory, and the data below were collected Speed x ||| 30 40 50 60 70 80 90 Mpg y ||| 39 38 36 32 27 24 22

i. Present a scatter plot for the data

ii. Determine the correlation coefficient for the data, and interpret the value.

iii. Determine the least-squares regression line.

iv. Estimate the gas mileage at 65 mph.

Answer 1

> x<-c(30,40,50,60,70,80,90)
> y<-c(39, 38, 36, 32, 27, 24, 22)
> plot(x,y)
> plot(x,y,xlab='Speed',ylab='Mileage')

> cor(x,y)
[1] -0.985349
> lmod1<-lm(y~x)
> lmod1

Call:
lm(formula = y ~ x)

Coefficients:
(Intercept) x
50.0000 -0.3143

ii. Correlation coefficient is = -0.985, (as found by R-code of part i)

Interpretation : With increase in speed, mileage decreases and the strength of this negative relation is very high equal to

- 0.985

iii. Least squares regression line is obtained by previous R-code , and obtained equation is :

y = 50 - 0.3143*x

iv. Now for x = 65, from above equation , estimate for y = 29.5705