Question

A department of transportation's study on driving speeds and miles per gallon for midsize automobiles resulted in the following data:
Speed (MPH)	Miles per Gallon
30	28
50	25
40	25
55	23
30	30
25	32
60	21
25	35
50	26
55	25
(a) Find the line of best fit
(b) Predict the mileage for a driving speed of 42 mph.
c) Compute and interprent the correlation coefficient.
(b) Is the relationship between speed and gas mileage statistically signficant? Provide support.

Answer 1

a)Codes:

Import the data set into R and store in a data frame dat

summary(lm(dat$`Miles per Gallon`~dat$`Speed (MPH)`))

Output:

Coefficients:

Estimate Std. Error t value Pr(>|t|)   

(Intercept) 39.01807 2.02017 19.314 5.36e-08 ***

dat$`Speed (MPH)` -0.28614 0.04598 -6.223 0.000253 ***

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.874 on 8 degrees of freedom

Multiple R-squared: 0.8288, Adjusted R-squared: 0.8074

F-statistic: 38.72 on 1 and 8 DF, p-value: 0.0002531

Result-

The regression model is given by Miles per Gallon=39.01807-0.28614*Speed(MPH)

b)The predicted value of Mileage for 42 MPH is 27.00019 Miles per Gallon

c)Correlation coefficient:

Code-cor(dat$`Speed (MPH)`,dat$`Miles per Gallon`)

Output:-0.9103694

Interpretation:Highly negatively correlated .Therefore,if the speed of automobiles increases the mileage decreases.

d)Since here the p value <0.05,hence the relationship between speed and gas mileage is statistically significant.