# Identifying trends when data points are averages with standard errors

I am trying to use a regression to identify trends in the poverty rate over time in county level Census data. I cannot use smaller geographies in my regression because the rates provided by Census tract do not cover all the groups I am looking at. I only have one data point for each year for the county, and it comes from the American Community Survey, so it is not a census and each data point has a SE. How should I approach the regression? A simple regression with one data point for each year would not reflect the unreliability of the underlying data. I was considering transforming each data point into n data points randomly distributed around the observed value according to its SE, but I am concerned that the extra data points will affect the p values. Is that the correct way to proceed or is there a better way?

• I think you are looking for some form of weighted regression where you weight the points inversely by their variance. – mdewey Aug 29 '16 at 14:58
• Wouldn't a weighted regression just equalized the SE between data points? My concern is more that a high SE in observations should increase the SE of the coefficient of time. For instance, say I'm seeing a poverty rate in one group rising from 20% to 25% over time in two groups. One group is large and the SE for the poverty rate is about 0.5% each year. But another group is small and has about a 10% SE for the poverty rate each year. The trend for the first group is significant, but not for the second group, and I'm not sure how to set up a regression to make that distinction. – Drevent Aug 29 '16 at 15:59
• @mdewey the points would need to be weighted by the county population, which complicates things. @drevent since you seem unmarried to counties, i recommend you switch to pumas and use R's svyglm command run directly on the acs microdata. asdfree.com/search/label/… – Anthony Damico Aug 30 '16 at 2:40
• @AnthonyDamico I am using PUMS data for some of my analysis, but try to use pre-aggregated ACS data when possible because the Census calculates these statistics using a larger population, and the SE is much lower for them. The SE for data aggregated using the PUMS is simply too high for me to use for some populations within the county. I think my options are some kind of regression on pre-aggregated county level data, compare the first and last year rates of pre-aggregated county level data, 1 year aggregated PUMS data with higher SE, and 5 year aggregate PUMS data with lower relevance. – Drevent Aug 30 '16 at 13:30