Distance from Salt Lake City

In “Church Growth by State,” I suggested that membership as a percent of a state’s population (density) is a function of, among other things, distance from Utah based on visual examination of the above graph.  Often, the eye can deceive when examining data statistical techniques must be employed to verify observations. Without getting too technical, my simple model which I will describe in a little more detail below, had statistical validity, explaining about 47.7% of the difference between the density of LDS population in a state.  Not bad for one variable, but what explains the remaining difference in density?

I suspect that it is relative economic growth.  Some states have grown faster economically.  The change in density caused by economic growth depends on the beginning density.  If a state like Idaho in which 26% of the residents are Mormons experiences rapid growth, those moving into the state are likely to reflect the nation as a whole in which only 2% of the residents are Mormons.  The influx of new residents will lower the density.  In a state like Georgia, in which .81% of the residents are Mormons experiences rapid growth, those moving into the state are likely to again reflect the nation as a whole in which 2% of the residents are Mormons.  The influx of new residents will raise the density.  As an aside, I tried using population growth for one year as a proxy for economic growth because I had that data but it was not statistically significant. 

For those interested in the stats, the model I used was

Density = b0 + b1*ln(distance) +e

Where density is the percent of a state’s population that is LDS, distance is the number of miles from a state’s largest city to Salt Lake City, b0 and b1 are coefficients, and e is the error term.

The F statistic for the equation was 41.03, R² was 47.7 and the t-statistics for the variables were 6.74 and –6.41.