# Correlation of Pavement Distress and Roughness Measurement
## 5 Raveling vs. IRI
### Distresses Density and the IRI Model
* Model-1 the linear regression equation for the first model that relates IRI against all apparent distresses: \[\text{IRI}=2.59+0.0422\text{ Cr}+0.0411\text{ Pa}+5.75\text{ Po}+1.32\text{ Dr}+0.00996\text{ Ra}\] (8)  
The estimated regression coefficients and the overall model statistics were shown in Table 4.  
The \(p\)-values for most of the regression coefficients are zero, clearly showing a significant linear correlation between the estimated values of IRI and the different types of distress. The \(p\)-value of the potholes (Po) coefficient is equal to 0.168, which is greater than the 0.05 level of significance therefore there is significant evidence to exclude the potholes coefficient which demonstrates no linear relationship between IRI and potholes distress. 1. Analysis of Variance  
Source DF SS MS F \(p\)  
Regression 5 70.405 14.081 17.56 0.000 Residual Error 134 107.463 0.802 Total 139 177.868 Based on the ANOVA-test results, the \(p\)-values for the values of IRI response variables are equal to zero, meaning that the regression model does not account for any statistically significant variance in the IRI response variables. Furthermore, the data give sufficient evidence of the presence of a dependence relationship between the value of IRI and distresses. \begin{table}
\begin{tabular}{c c c c c} \hline
**Predictor** & **Coef.** & **St.Dev.** & **T** & \(\boldsymbol{p}\) \\ \hline Constant & 2.594 & 0.1317 & 19.7 & 0 \\ Cr & 0.042227 & 0.00892 & 4.73 & 0 \\ Pa & 0.04107 & 0.01259 & 3.26 & 0.001 \\ Po & 5.752 & 4.146 & 1.39 & 0.168 \\ Dr & 1.3185 & 0.4064 & 3.24 & 0.001 \\ Ra & 0.009962 & 0.005005 & 1.99 & 0.039 \\ \hline \end{tabular}
\end{table} 
Table 4: Summary of t-test for secondary streets (Model-1). Squared multiple correlation coefficient (R2): R-Sq = 38.7% R-Sq(adj) = 36.9%  
The value of the squared multiple correlation coefficient (R2) is 36.9%. This means that 36.9% of the IRI values can be described by the regression model. This shows adequate logic of the regression model relating IRI and distress data. Model-2 the linear regression equation for the second model that relates IRI vs. ride quality distresses:  
\[\text{IRI}=2.5889+0.043121\text{ Cr}+0.04366\text{ Pa}+1.3193\text{ Dr}+0.010589\text{ Ra} \tag{9}\]  
The estimated regression coefficients and the overall model statistics were shown in Table 5.  
In this case, the \(p\)-values for all ride quality regression coefficients are equal to zero, meaning that there is strong evidence to accept the regression coefficient of all distress densities in the regression model with 95 percent confidence. This indicates a statistically significant linear association between the different types of ride quality distresses and IRI ratings. 1. Analysis of Variance  
Source DF & SS & MS & F & \(p\) Regression & 4 & 68.861 & 17.215 & 21.32 & 0.000 Residual Error & 135 & 109.007 & 0.807 Total & 139 & 177.868 According to the ANOVA-test results, the \(p\)-values for the response variable is equal to zero, meaning that there is no significant amount of variation within the response variable in the regression model. The data reflect sufficient evidence of a dependent relationship between IRI and distressed values. Note that the F-value for model-2 = 21.32, which is greater than the F-value from model-1 which = 17.56, demonstrating an improvement in model-2 over model-1. Squared multiple correlation coefficient (R2): R-Sq = 39.6% R-Sq(adj) = 37.3%  
The value of the squared multiple correlation coefficient (R2) equals 37.3% which means that 37.3 percent of the IRI values are described and evaluated by the regression model showing adequate logic of the regression model relating IRI and distress data. Note that R2 in the second model (37.3) is greater than the first one (36.9) indicating an improvement of model-2 over model-1. It also shows that while there are statistically significant correlations between IRI and some types of distress, these relationships aren't strong enough for distress types to be used as a predictable measure for roughness conditions.