Interpreting the resultsOrdinal Logistic Regression: OrdinalYears versus Adj_Forty Link Function: LogitResponse InformationVariable Value CountOrdinalYears 0 9 1 10 2 11 Total 30Logistic Regression Table Odds 95% CIPredictor Coef SE Coef Z P Ratio Lower UpperConst(1) -3.66970 3.35366 -1.09 0.274Const(2) -2.25094 3.30836 -0.68 0.496Adj_Forty 0.0292074 0.0342799 0.85 0.394 1.03 0.96 1.10Log-Likelihood = -32.529Test that all slopes are zero: G = 0.659, DF = 1, P-Value = 0.417Goodness-of-Fit TestsMethod Chi-Square DF PPearson 60.2893 57 0.358Deviance 65.0573 57 0.217Measures of Association:(Between the Response Variable and Predicted Probabilities)Pairs Number Percent Summary MeasuresConcordant 170 56.9 Somers' D 0.15Discordant 125 41.8 Goodman-Kruskal Gamma 0.15Ties 4 1.3 Kendall's Tau-a 0.10Total 299 100.0Interpreting the resultsResponse Information displays the number of observations that fall into each of the response categories, and the number of missing observations. The ordered response values, from lowest to highest, are shown. Here, we use the default coding scheme which orders the values from lowest to highest: 0 is zero years in NFL, 1 = more than zero but not more than 3 years, and 2 = more than three years.Logistic Regression Table shows the estimated coefficients, standard error of the coefficients, z-values, and p-values. When you use the logit link function, you see the calculated odds ratio, and a 95% confidence interval for the odds ratio.- The values labeled Const(1) and Const(2) are estimated intercepts for the logits of the cumulative probabilities of survival for 0 years, and for 0 to 3 years, respectively. Because the cumulative probability for the last response value is 1, there is not need to estimate an intercept for more than 3 years.1- There is one estimated coefficient for each covariate, which gives parallel lines for the factor levels. Here, the estimated coefficient for the single covariate, Adj_Forty, is 0.0292, with a p-value of 0.394. The p-value indicates that for most --levels, there is insufficient evidence to conclude that the adjusted forty time affects years in NFL. The positive coefficient, and an odds ratio that is greater than one indicates that higher adjusted forty times tend to be associated with lower values of NFL years. Specifically, a one-unit increase in adjusted forty time results in a 3% increase in the odds that a player serves 0 years versus greater than 3 years and that the player serves less than or equal to 3 years versus greater than 3 years.- Next displayed is the last Log-Likelihood from the maximum likelihood iterations along with the statistic G. This statistic tests the null hypothesis that all the coefficients associated with predictors equal zero versus at least one coefficient is not zero. In this example, G = 0.659 with a p-value of 0.417, indicating that there is insufficient evidence to conclude that at the estimated coefficient is different from zero.Goodness-of-Fit Tests displays both Pearson and deviance goodness-of-fit tests. In our example, the p-value for the Pearson test is 0.358, and the p-value for the deviance test is 0.217, indicating that there is insufficient evidence to claim that the model does not fit the data adequately. If the p-value is less than your selected --level, the test rejects the null hypothesis that the model fits the data adequately.Measures of Association display a table of the number and percentage of concordant, discordant and tied pairs, and common rank correlation statistics. These values measure the association between the observed responses and the predicted probabilities.- The table of concordant and discordant pairs and tied pairs is calculated by pairing the observations with different response values. Here, we have nine 0's, ten 1's, and eleven 2's, resulting in 9 x 10 + 9 x 11 + 10 x 11 = 299 pairs of different response values. For pairs involvingthe lowest coded response value (the 0-1 and 0-2 value pairs in the example), a pair is concordant if the cumulative probability up to the lowest response value (here 0) is greater for theobservation with the lowest value. This works similarly for other value pairs. For pairs involving responses coded as 1 and 2 in our example, a pair is concordant if the cumulative probability up to 1 is greater for the observation coded as 1. The pair is discordant if the opposite is true. The pair is tied if the cumulative probabilities are equal. In our example, 56.9% of pairs are concordant, 41.8% are discordant, and 1.3% are ties. You can use these values as a comparative measure of prediction. For example, you can use them in evaluating predictors and different link functions.- Somers' D, Goodman-Kruskal Gamma, and Kendall's Tau-a are summaries of the table of concordant and discordant pairs. The numbers have the same numerator: the number of concordant pairs minus the number of discordant pairs. The denominators are the total number of pairs with Somers' D, the total number of pairs excepting ties with Goodman-Kruskal Gamma, and the number of all possible observation pairs for Kendall's Tau-a. These measures most likely lie between 0 and 1 where larger values indicate a better predictive ability of the