# Analysis of approval rating data

Rich Harang says: Approval rating data has been collected from Real Clear Politics,summarizing President Obama's approval ratings from the end of January, 2009, through present day. We have collected a subset from five different polling organizations (CBS, CNN, FOX news, Gallup, and Rassmussen; all of which were selected on the basis that they had more than 15 samples available) from January 2009 through the present (see figure).

There are clear poll-to-poll biases: Rassmussen, for instance, appears to be consistently lower than the bulk of the other pollsters, while CNN appears to trend higher than the rest. These biases appear to be fairly consistent over time, however we would like to quantify them, see if they drift over time, and try to find the "true" approval rating for President Obama over time based on this sparse data.

As the data appears to have "momentum", we will fit a local linear model, in which the slope of the approval rating changes over time, and apply a linear model to account for pollster biases. Due to the large sample sizes, we can treat the data as approximately normal, and due to the consistent polling sizes and popluations for each pollster (e.g. Rassmussen typically samples 1500 likely voters over the course of 4 days, while FOX news typically samples 900 registered voters over 2 days), we can treat the variance for each pollster as fixed but unknown.

Rigorous eyeball-based analysis suggests that our model should predict a mean approval rating of roughly 0.47 at a three-week horizon, and 0.41 or so at a three-month horizon. The actual observed data point will depend on the poll used, however we may guess that any Rassmussen poll will likely be 3-5 points below the mean, and a CNN poll will likely be 1-2 points above the mean.

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