In March 2006, The Economist reported results for number of blades per razor by

Question

In March 2006, The Economist reported results for number of blades per razor by year of introduction (http://www.economist.com/node/5624861 ). Based on the data in the article,

Razor

Year

Blades per Razor

Gillette Safety Razor

1901

1

Gillette Trac II

1971

2

Gillette Mach III

1998

3

Schick Quattro

2003

4

Gillette Fusion 5

2006

5

For the power law model, which razor was the largest outlier?

A. Gillette Safety Razor

B. Gillette Trac II

C. Gillette Mach III

D. Schick Quattro

E. Gillette Fusion 5

Razor

Year

Blades per Razor

Gillette Safety Razor

1901

1

Gillette Trac II

1971

2

Gillette Mach III

1998

3

Schick Quattro

2003

4

Gillette Fusion 5

2006

5

Explanation / Answer

The power law model

y =abx

ln y = ln a + x ln b

taking linear regression equation between ln y and x

calculating linear regression equation for it

lny = -26.37 + 0.01382 x

so now we see the outlier here.

Here the maximum deviation is for Gillete fusion 5. which is 0.2340.

So THe answer is option 5.  

Razor Year ln (Razor) =y y' y - y' Gillette Safety Razor 1901 0 -0.07697 0.076968 Gillette Trac II 1971 0.693147 0.891272 0.198125 Gillette Mach III 1998 1.098612 1.264736 0.166124 Schick Quattro 2003 1.386294 1.333896 0.052398 Gillette Fusion 5 2006 1.609438 1.375392 0.234046

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