Output of theReport
The diagnosticplots for this model look better than before we took the transforms.Therefore, we can say that the residuals are well behaved, since theyappear unbiased and homoscedastic. The Q-Q plot indicates a smallamount of skewness that is inclined to the right. There also existsan outlier from the Q-Q plot as depicted at the right top of theoutput graph. The cook’s distance vs. leverage plot outlines thatobservation 26 appear to have relatively high cook’s distances andhigh levels of leverage, thereby standing out clearly as a possibleoutlier.
From the output of the influencepoints, it is clear that observations 15, 25 and 51 appearproblematic to our model. These observations either have highleverages or even large residuals. The cook’s distance indicatesthat observation 15 and 25 are not as influential as observation 26,this is due to the fact that, observation 26 has relatively highcook’s distance compared to the other two observations which havelow distances.
INFLUENCE POINTSLet’slook at the influence points:
## Potentiallyinfluential observations of##lm(formula =log(Firearm.related) ~ log(Gonorrhea.in.Females) + Teen.Birth.Rate +log(Infant.Mortality.Rate) + Dependency) :## ## dfb.1_dfb.l(G. dfb.T.B. dfb.l(I. dfb.Dpnd dffitcov.rcook.d hat##15 -0.27 -0.24 0.26 0.48 -0.02 -0.84 0.67_* 0.13 0.10## 25 0.250.24 0.69 -0.43 -0.55 -0.97_* 0.86 0.17 0.17## 26 0.43 -0.98 0.65 1.55_* -0.83 -1.78_* 1.39_* 0.60 0.45_*## 38 -0.03 -0.01-0.01 0.02 0.02 -0.04 1.35_* 0.00 0.18
It is important to note that thehigher the cook’s distance is, the more influential the point is.From the output of potentially influential points above, all the fourobservations indicates cook’s distances that are lower than 1thereby implying that as much as there seems to be some influence,the influence are not very extreme. Further to this, the observationsdepicts varying levels of leverages as is analyzed bellow.
Observation 26 has the largestleverage and the largest residual. As a result, this combination ofhigh residuals and high leverage is what has made this observationvery influential in the model. On the other hand, observation 15 hasthe lowest leverage and lowest residual, this low leverage makes theobservation less influential. Observation 38 has a relatively highleverage and the second largest residual, however, this observationhas the least influence in the model.
Using the df values from theoutput, we can say that after the transformation, the coefficient forgonorrhea in observation 15 for female decreases by -0.24 standarderrors, teens birth rate increases by 0.26, infant mortality rateincreases by 0.48 and that of dependency rate reduces by -0.02standard errors as compared to before the transformation.