STANDARD ERROR: Linear Regression Trendline?

Question

CAVEAT: I have a limited knowledge of statistics and and am not particularly adept with respect to formulas. Hence, kindly explain using prose if you would.

ISSUE: Using stock trading software by prophet.net, a 64-day Linear Regression Trendline ("LRT") is currently the best fit for a particular stock. The 64-day LRT has an R-squared of .933. Now, the trading software has an indicator called "Standard Error Bands" which allows you, for example, to enter (64,3), (64,2), (64,1) etc. In this example, of course, the indicator plots "standard error band" values ("SE") (3SE, 2SE, 1SE etc.) both above and below the 64-day LRT.

With all this in mind, I have researched how to calculate "standard error" but my results don't seem to match the trading software. The trading software determines the 64-day LRT by using the CLOSING prices for the last 64-days. Can someone give me a step-by-step on how to calculate the 1SE of the 64-day LRT. ASSUME THAT I ALREADY HAVE THE LRT VALUE--I do.

It's my understanding that the "Standard Error" is the "Standard Deviation" divided by the square root of the number of samples. I tried taking the Standard Deviation of the Closing Prices over the last 64 days and, alternatively, the Standard Deviation of the 64-day Linear Regression Trendline itself--both of which come out to 3.15 and 3.18 respectively, and then divided both of those numbers by 8, which gives me a value of .39 or so for 1 Standard Error. The software, however, has a value that is much greater--closer to .80.

Answer 1

Remember, your LRT is simply a best fit line.

A line is of the form y = mx + b.

Your software is taking all the points and determining the "best" values for both m, the slope, and b, the y intercept.

This is a *two variable* problem, so it's not just simply the square root of the number of samples.

Instead, you have to use the following formula:

SE = Standard Dev of the sample / sqrt (x - x(mean)) [summed]

SE = 3.15 /...

So for the denominator, you will take your first x value, and subtract the mean. You will take your second x value, and subtract the mean, you will do the same for your third, fourth etc all the way to 64 and add them all up. Then, take the square root of that.

Let me know how it goes.

Regards,

Mysstere

Answer 2

the blunders could be based on your style line. as you're utilising that to forecast previous the tip of your records. and you form of do away with your blunders bands or something like that by utilising doing the rage line or are you not utilising OLS. and that i dont think of multiplying your STD will do plenty besides supply you a larger form. the STD is a function of the variance over the line so multipling it won't do plenty for you. yet do you certainly choose STD off the rage line or off the bell curve distribution. in case you opt for it off the rage line you employ the rage line as a advise for the distibutions and create it off that then you definately've a one 2 and 3 STD lines. been so long for the reason that i did it by utilising hand not sure how its executed on paper.