The analemma and the equation of time result from the sum of the Earth's elliptical orbit around the Sun and the tilt of the Earth's axis in relation to the plane of its orbit around the Sun. The following graph shows the effect of this summation. Note that the summation of both effects results in a curve that is more similar to the graph obtained as a result of the Sun's shift due to Earth's tilt. Hence, the Earth's tilt has a greater effect on the analemma than its elliptical orbit.
From the above graph, we get the following analemma curve.
The above chart shows the position of the true sun in the sky throughout the year. The y-axis on the chart represents the declination of the Sun in the sky for one year, going from -23.5° in the winter to +23.5° in the summer. The x-axis represents the difference in time from what your watch reads to the actual position of the Sun in the sky.
Let's go back to the celestial sphere and watch the path of the true sun making the analemma curve. The speed of the true sun on the ecliptic reflects its elliptical orbit around the Sun, moving faster in January and slower in July.
Click here for the animation.