Sample: Polls of likely voter with fieldwork completed after July 4th; includes 119 polls from 2008 and 47 from 2012. Last 2012 observation is Pew on October 7th.
Polls are dated by the close of fieldwork (called the “polling date” in this blog). The independent variable “Days Before” in the models below is the number of days between the polling date and each year’s Election Day.
The dependent variable “Obama Lead” is the signed difference in voting intention between President Obama and his Republican opponents.
Results for Graph Entitled: “Support for Obama Grows as Election Days Near”
Dependent variable: Obama Lead coefficient std. error t-ratio p-value ---------------------------------------------------------- Constant 7.12852 0.437479 16.29 4.07e-36 *** Days Before −0.0658809 0.00875104 −7.528 3.24e-12 *** Mean dependent var 4.536145 S.D. dependent var 4.020616 Sum squared resid 1982.247 S.E. of regression 3.476618 R-squared 0.256829 Adjusted R-squared 0.252298
The constant measures the expected size of Obama’s lead on Election Day, when Days_Before is by definition zero. In this case the model predicts a 7.1% lead on Election Day, three-tenths of a point below the President’s actual two-party margin of victory of 7.4%. Our level of confidence in this figure is quite high given its estimated standard error of 0.44. The 95% confidence interval for our Election Day estimate is that Obama will be leading in the polls by a figure somewhere between 6.3% and 8.0%.
It takes 1/0.0658809, or a bit over fifteen days, for Obama to gain a full percentage point in the polls.
Results for Graph Entitled: “Small Differences Found for 2012”
Dependent variable: Obama Lead coefficient std. error t-ratio p-value ---------------------------------------------------------- Constant 7.16113 0.435755 16.43 2.04e-36 *** Days Before −0.0589353 0.00969621 −6.078 8.32e-09 *** 2012 −1.08048 0.663637 −1.628 0.1054 Mean dependent var 4.536145 S.D. dependent var 4.020616 Sum squared resid 1950.527 S.E. of regression 3.459252 R-squared 0.268721 Adjusted R-squared 0.259749
This model includes a dummy variable for the 2012 election, allowing the intercept to shift depending on the year. The estimated shift is about one percentage point in the Republican direction, though the difference between the elections shows only marginal statistical significance with a p of 0.105.
Test for Difference in Both Slope and Intercept in 2012
Dependent variable: Obama Lead coefficient std. error t-ratio p-value ---------------------------------------------------------- Constant 7.33871 0.465538 15.76 1.57e-34 *** Days Before −0.0646965 0.0110624 −5.848 2.66e-08 *** 2012 −2.41672 1.40387 −1.721 0.0871 * DayB4*2012 0.0247756 0.0229408 1.080 0.2818 Mean dependent var 4.536145 S.D. dependent var 4.020616 Sum squared resid 1936.584 S.E. of regression 3.457488 R-squared 0.273949 Adjusted R-squared 0.260503
The last variable is the product of days before the election and the 2012 dummy variable. If this coefficient were to prove signficant, that indicates that the trend in Obama’s support is following a different trajectory than in 2008, growing either faster or slower than four years ago. So far there is no statistical evidence for a divergent trajectory; at best we see the marginally significant difference of a flat one percent in polls of likely voters taken since the Fourth of July. I will be updating this finding as we approach Election Day.
