Question

15. Pizza and the Subway Use the pizza costs and subway fares to find the best predicted subway fare, given that the cost of a slice of pizza is $3.00. Is the best predicted subway fare likely to be implemented? Year Pizza Cost Subway Fare CPI 1960 0.15 0.15 30.2 1973 0.35 0.35 48. 3 1986 1.00 1.00 112.3 1995 1.25 1.35 162.2 2002 1.75 1.50 191.9 2003 2.00 2.00 197.8 2009 2.25 2.25 214.5 2013 2.30 2.50 233.0 2015 2.75 2.75 237.2

Please explain in detail. Thank you.

Answer 1

Note: All the work has been done in excel

First, we find the correlation between pizza cost and subway fares which comes to be r = 0.99175 which indicate a strong positive linear relationship exists between our two variables.

	Column 1	Column 2
Column 1	1	0.991745
Column 2	0.991745	1

Next, we tried to fit the best-predicted regression line. Here is the snapshot of the results.

	Coefficients
Intercept	-0.011089825
Pizza Cost	1.010855683

Regression Statistics
Multiple R	0.991745315
R Square	0.983558769
Adjusted R Square	0.981210022
Standard Error	0.126181999
Observations	9

Pizza Cost Line Fit Plot 3 2 subway fare 1 Predicted subway fare 1 2 Pizza Cost subway fare

The regression line thus obtained is (see table above)

subway fare = -0.01108 + 1.0108*pizza cost

Hence when pizza cost =3

subway fare= 3.021

The above regression line explains 99% variability within the data. ( see R square value)

But the predicted x value (pizza cost=3) lie beyond the data point and thus cannot be predicted and used further with greater confidence. However other techniques such as forecasting( extrapolation) can be used here to find values beyond our data point.