An origin-destination survey in 10 travel-analysis zones provided the following data on zonal residential densities (households/acre) and average daily trip productions per household:
Density X: 42 5 25 10 4 15 20 12 14
22
Trip Rate Y: 1.5 4 2.1 2.6 4.8 2 2.5 3.3 1.9
2
Use the method of least squares to develop a regression model for predicting trip production rates as a function of density.
a. Plot the data and the model.
b. How good is a fit?

a)

b)  

For our case we have this:

n=10  

And the variation coeffcient would be

And we can conclude that the linear model explains 57.9 % of the variation.

Explanation:

a. Plot the data and the model.

Data given:

X: 42 5 25 10 4 15 20 12 14  22

Y: 1.5 4 2.1 2.6 4.8 2 2.5 3.3 1.9  2

For this case we need to calculate the slope with the following formula:

Where:

So we can find the sums like this:

With these we can find the sums:

And the slope would be:

Nowe we can find the means for x and y like this:

And we can find the intercept using this:

So the line would be given by:

The plot on this case is on the figure attached.

b. How good is a fit?

For this case we can calculate the correlation coefficient with the following formula:

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.

And in order to calculate the correlation coefficient we can use this formula:  

For our case we have this:

n=10  

And the variation coefficient would be

And we can conclude that the linear model explains 57.9 % of the variation.

answer: 500 wph.

explanation: