Evaluating Human Services Performance across Counties: A Multiple Regression Analysis (MRA) Demonstr
The Minnesota Department of Human Services used a Multiple Regression Analysis (MRA) to “level the playing field” and determine the performance ranges of each of the human service agencies in 84 counties and cooperative of counties in the state. With data derived in its 2010 publication (1), we hope to show the concept of this powerful analytical tool. MRA is an extension of the simple regression analysis (SRA) where instead of one independent explanatory variable, there would be two or more. This statistical analytics tool is also powered by a mathematical procedure that fits a line through the “hyperplane” with the least deviation from each observed data. As with the SRA, this analytical tool uses the regression add-in in everybody’s copy of Microsoft Excel.
The administrator discusses with the assistant administrator, Lamar Smith, the result of an analysis by Geena, the County’s director of social services and Chad, a social service area case manager. “They established that human services funding in each Minnesota County is statistically associated with its population of residents. We know that each county is different, so we have to reduce the uniqueness of each county by looking at the correlation of available demographic variables correlated to the actual total human resources funding. In a nutshell, we will be estimating Y for our county and every other county in Minnesota, that total human resources funding for the conceptual and non-observable real need ,Y’, as shown in the diagram above. Operationally, we will be able to forecast future service delivery funding needs with finer measurable demographic factors. We also will know whether the needs of our residents are adequately funded.” Lamar responded with, “I will be back with my analysis in four days to share with you and our strategic planning committee.”
In his analysis Lamar said, “the basic assumption of my analysis is that the funding of non-observable real needs, Y’, can be estimated estimated by observable and measurable variables, X1, X2 and X3 surrogate to non-observable variables, x2’, X4’ and X6’. I run MRA on several sets of demographic variables resulting in the following best regression equation:
This estimator equation gave the best combination of: multiple regression coefficient, R2; calculated p; appropriate signs of intercept and variables; and standard error. The variable set I finally was satisfied with was:
Actual HS Funding - 5-year Average of Human Services Funding for each County/Agency.
Population Density - Estimated Residents per Square Mile in 2006.
Extent of Poverty - Estimated Residents Living in Poverty in 2004.
Residents on Disability - Estimated Residents that Received a Federal Disability Determination in 2006.
Non-English Speaking Residents - Estimated Residents that Did Not Speak English Well or Not at All in 2000.
My analysis indicated potential capacity for certain counties to accommodate more clients with their actual human services funding. Our county is not one of those with unused capacity. Minnesota counties listed have potential capacity as their actual funding was more than 75% of standard error from their estimated human services funding.”
(1) The source of data used in this demonstration came from Minnesota Department of Human Services’ January 2010 publication: “2009 Report on Human Services Performance, Selected County Measures.” The data set is available from mgmtlaboratory.com upon request.
By Noel Jagolino, contributing management consultant