Question

Solve problem (P4.2) from the textbook using the following data instead of the data given in the textbook. Solve only requirements under a, b and c. Show your assumptions and consequent calculations on how you catered for the fact that 1997 means first half of the year and 1997.5 means in the second half of the year; without such initial, your solution will not be considered as your own.   (Hint: you may use Excel or any software to conduct linear regression/linear curve fitting. Note also that ‘condition’ should be related to age and not the date).

Show the details of your ‘software’ analysis and calculations.

Date	Condition
1985	1
1985.5	1
1996.5	2
1997	2
1997.5	2
1998	2
1998.5	2
1999	2
1999.5	3
2000	3
2000.5	3
2001	4
2001.5	4
2002	4
2002.5	4
2003	4

This is the book Q :

Appearing below is a series of roof inspection condition summaries, where 1 is excellent and 5 is poor. Note that an inspection 1997.5 occurred in the second six months of 1997, whereas 1997 occurred in the first six months of 1997. The roof was replaced in 1985. Answer the questions below. You might use software aids, such as EXCEL or MATLAB, for this problem.
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a. Estimate an ordinary least squares regression deterioration model of the form: Condition = a + b(age) where age is the age of the roof in years. Report your parameter estimates, standard errors, t-statistics and R^2 values. Note that there is a gap in the data from 1985 to 1996! b. Suppose I have a comparable roof that is 12 years old. What would your regression model in (a) predict for its condition? What would it predict for age 18? At what age is condition expected to become 5? c. Plot the data and your regression line.

course: Infrastructure managment

Answer 1

Analysing the trend in the data, there is a gap in the data from 1985 to 1996 which is significantly big.

So instead of filling in these datapoints by aggregating, it is safe to omit the datapoints before 1996 as they are minor outliers.

Another heuristic we are going to apply is to subtract 1995 from all the year values to make it start from 1. The final data will look like this :

Period	Condition
1	2
2	2
3	2
4	2
5	2
6	2
7	3
8	3
9	3
10	4
11	4
12	4
13	4
14	4

Plotting this data for regression model, we get :

The parameter estimates are :

Slope:0.2044
Intercept:1.3956

R-Square Value : 0.8697

The equation is :

Predicted Value(Age) = Intercept + Slope(Age)

For a roof that is 18 years old, in our model, the Age = 18-12 = 6.

Predicted Condition = 1.3956 + 0.2044 x 6

= 2.622 which is rounded to 3

For a roof to reach a condition value of 5,

5 = 1.3956 + 0.2044 x Year

Year = (5 - 1.3956 ) / 0.2044 = 17.63 = 18

Hence Age = 18 + 12 = 30

Therefore roof must be 30 years old.