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

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

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