7.25 Answer Presentation

A. Joshua Bentley
November 28, 2018

Question Overview


7.25 The Coast Starlight, Part II

The Coast Starlight Amtrak train runs from Seattle to Los Angeles.

  • The mean travel time from one stop to the next on the Coast Starlight is 129 mins, with a standard deviation of 113 minutes.

  • The mean distance traveled from one stop to the next is 108 miles with a standard deviation of 99 miles.

  • The correlation between travel time and distance is 0.636.

a) Write the equation of the regression line for predicting travel time.

1 of 3

Target Mean StDev . Other.Metrix X_
time (as y) 129 113 Correlation 0.636
distance (as x) 108 99

Equation for slope using Standard Deviation

b-sub_1 = \( \frac{S_y}{S_x} \cdot \) R

b = \( \frac{113}{99} \cdot \) 0.636

Slope(b) = 0.726

a) Write the equation of the regression line for predicting travel time.

2 of 3

Target Mean StDev . Other.Metrix X_
time (as y) 129 113 Correlation 0.636
distance (as x) 108 99 Slope 0.726

Slope-point equation for regression line

y - y-sub_0 = slope \( \cdot \) ( x - x-sub_0 )

129 - y = 0.726 \( \cdot \) (108 - x)

129 - y = 78.41 - 0.726x

a) Write the equation of the regression line for predicting travel time.

3 of 3

Target Mean StDev . Other.Metrix X_
time (as y) 129 113 Correlation 0.636
distance (as x) 108 99 Slope 0.726

Slope-interept equation for regression line

129 - y = 78.41 - 0.726x

-y = -50.59 - 0.726x \( \Rightarrow \) y = 0.726x + 50.59

b) Interpret the slope and the intercept in this context.

Target Mean StDev . Other.Metrix X_
time (as y) 129 113 Correlation 0.636
distance (as x) 108 99 Slope 0.726
y intercept 50.590

The line has a slope of 0.726 and will cross the y axis when y = 50.59.

This means that the train travels at approximately 0.726 minutes per mile.

c) Calculate R2 of the regression line for predicting travel time from distance traveled for the Coast Starlight, and interpret R2 in the context of the application.


Correlation \( R \) is 0.6362 so \( R \)2 is .405, meaning that about 41% of travel time is explained by distance.

d) The distance between Santa Barbara and Los Angeles is 103 miles. Use the model to estimate the time it takes for the Starlight to travel between these two cities.


y = 0.726x + 50.59

y = (0.726)(103) + 50.59

y = 125.4 minutes

e) It actually takes the Coast Starlight about 168 mins to travel from Santa Barbara to Los Angeles. Calculate the residual and explain the meaning of this residual value.


The residual for this point is 42.6 meaning that the predicted value was 42.6 minutes less than the actual observation.

f) Suppose Amtrak is considering adding a stop to the Coast Starlight 500 miles away from Los Angeles. Would it be appropriate to use this linear model to predict the travel time from Los Angeles to this point?

In general we can see that the question is asking us to predict a value that lies outside the population from which samples are available and thus, ultimate, the answer is no, it would need to be extrapolated.