The operational performance of service systems is commonly measured with key performance indicators (KPIs), e.g., time-to-resolve, SLA compliance, and workload balance. The assumption is that healthy KPIs lead to healthy business outcomes such as customer satisfaction, cost savings, and service quality. Although the domain experts have an intuitive understanding of the causal relationships among the KPIs, the degree of influence a cause KPI has on the effect KPI is difficult to estimate based on intuition. Also, the intuitive understanding could be wrong. Further, we show how the causal relationships are intricate with aspects such as the rate of influence and conditionality in measurements. As a result, although crucial, it is nontrivial to estimate the degree of influence. Without the degree of influence, prediction of business outcomes and decisions based on them tend to be ad hoc. This paper presents a novel method for validating the intuitive direction and the polarity of a causal relationship provided by domain experts. Further, the method also estimates the degree of influence based on the measure of Pearson's correlation. Using the degree of influence and least squares regression, the method predicts values of effect KPIs. The method is evaluated by applying it on 10 widely used KPIs from 29 real-life service systems. We find that the method validates 8 of the 15 intuitive relationships and estimates the degree of influence for each of the validated relationships. Further, based on the degrees of influence and the regression model learned from the 29 service systems, the method could estimate the values of the effect KPIs with an average root-mean-squared error (RMSE) of 1.2%, in 9 additional service systems.