Chapter 10. Choosing the function behind the data
1. Can you find a better function?
In chapter 9 (‘Edmonton All, Urban, and Suburban.xls’) the model equation was
𝛽0 × (𝑀𝑎𝑗𝑜𝑟 𝑅𝑜𝑎𝑑 𝐴𝐴𝐷𝑇)𝛽1 × (𝑀𝑖𝑛𝑜𝑟 𝑅𝑜𝑎𝑑 𝐴𝐴𝐷𝑇)𝛽2 .
With this model equation the CURE plots for the ‘Urban’ and the ‘Suburban’
intersections are in Figures 1 and 2.
200
Urban
150
100
50
Cumulative
0
Residuals
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
-50
-100
-150
-200
X1, normalized Major AADT
200
Urban
150
100
50
Cumulative
0
Residuals
0.0
0.2
0.4
0.6
0.8
-50
-100
-150
-200
X2, normalized Minor AADT
Figure 1
1.0
1.2
400
Suburban
300
200
100
Cumulative
0
Residuals
0.0
0.2
0.4
0.6
0.8
1.0
1.2
-100
-200
-300
-400
X1, normalized Major AADT
400
Suburban
300
200
100
Cumulative
Residuals
0
0.0
0.2
0.4
0.6
0.8
1.0
-100
-200
-300
-400
X2, normalized Minor AADT
Figure 2
a. Blind search
Select a few functions to see if they improve the fit. If yes, determine whether the
addition of parameters is justified.
b. Interpret CURE plot deficiencies and use it to guide the search for more suitable
functions.
c. Check to observed/fitted ratios to find a suitable multiplier function.
d. Broaden your search by examining the fit of the Swedish model :
𝑀𝑖𝑛𝑜𝑟
𝛽2
𝛽0 (𝑀𝑎𝑗𝑜𝑟 + 𝑀𝑖𝑛𝑜𝑟)𝛽1 × (𝑀𝑎𝑗𝑜𝑟+𝑀𝑖𝑛𝑜𝑟) .