What Moving Average Formula does Google Sheets Use in Their Chart Trendline? I'm trying to come up with a formula that mimics the "Moving Average Trendline" that is provided in the Google Sheets Charts.
I've tried using a 3 month moving average, but it's not as good as Google's trendline.
Please check this sheet for a visual. 


*

*mg is the real data

*the lime green line is Google Chart's trendline feature

*3m SMA is my attempt at replicating their logic


Notice how much closer Google's trendline (lime green line) is to the series (mg) than the my formula (3m SMA) is.
here's a screenshot of the comparison between google and my function

and this how to find the trendline setting once you open up the chart settings

 A: Thanks to @cwindolf for the main leg work on this.
This is how I was able to get it to be exactly the same as their trendline. 
It consists of 3 parts.


*

*the start value from the original data series

*a 2 month moving average

*forecasting using simple linear regression


1. Start value
We simply just use the same value from original the series
C0=B0
2. 2 month moving average
Average y values from the same index as the original series, and the index before it
Ci=AVERAGE(B(i-1):Bi) (thanks to @cwindolf)
3. forecasting using simple linear regression
We'll be using this formula to calculate our $y$
$$
y=\alpha +\beta x
$$
where $\alpha$ is
$$
\alpha =\bar{y}-\beta \bar{x}
$$
and $\beta$ is
$$
\beta=\frac{\sum(x_{i}-\bar{x})(y_{i}-\bar{y})}{\sum(x_{i}-\bar{x})^{2}}
$$
Google Sheet's formula for C5's $\beta$ is =SUM(ARRAYFORMULA((A3:A4-AVERAGE(A3:A4))*(B3:B4-AVERAGE(B3:B4)))) / SUM(ARRAYFORMULA((A3:A4-AVERAGE(A3:A4))^4))
and the formula for C5's $\alpha$ with $\beta$ subbed in is =SUM(ARRAYFORMULA((A3:A4-AVERAGE(A3:A4))*(B3:B4-AVERAGE(B3:B4)))) / SUM(ARRAYFORMULA((A3:A4-AVERAGE(A3:A4))^2))
bringing it all together for C5($y$) we get
=AVERAGE(C3:C4)-(SUM(ARRAYFORMULA((A3:A4-AVERAGE(A3:A4))*(C3:C4-AVERAGE(C3:C4)))) / SUM(ARRAYFORMULA((A3:A4-AVERAGE(A3:A4))^2))*AVERAGE(A3:A4))+(SUM(ARRAYFORMULA((A3:A4-AVERAGE(A3:A4))*(C3:C4-AVERAGE(C3:C4)))) / SUM(ARRAYFORMULA((A3:A4-AVERAGE(A3:A4))^2))*A5)
To see it in action and to see a breakdown check out the SOLUTION sheet in this google sheet
