Probability of regression result

#1
Hi!

A stock is selling at $50 now. Based on a 90-day linear regression (i.e., 90 historical periods), 80 days from today, the stock will be selling at $56. The standard error is 4. What is the 95% probability that the stock will be selling at least at $59? Using Excel, how is the 95% probability calculated?

Thank you!

Tony
 
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#2
This is a hw problem. You can show some effort by posting your thoughts or you can just google for "linear regression prediction interval".
 

ondansetron

TS Contributor
#3
You probably also need to account for autocorrelation of errors if the experimental unit is a unit of time, which it sounds like the case. Without this the estimates may be incorrect. I would also be careful of misinterpreting a CI or PI as a "95% probability" interval.
 
#5
If it's not an idealized hw problem, then linear regression is far from being appropriate. First, you need to transform the data into returns, log-returns or some other weakly stationary stochastic process. Second, you need to apply time series techniques. In particular, as ondansetron pointed out, serial correlation may be an issue. Heteroskedasticity may be an issue as well.

The truth is: on 90 observations only, you will not develop a model sufficient for answering the question terribly accurately. And Excel is not software appropriate for time series analysis (everything is possible but painfully). If you are interested in statistical modeling, get R, Matlab, Stata or SPSS (in my humble opinion).
 
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#6
Dear Staassis,

Thank you for your reply.

I started with simple linear regressions, before getting into more sophisticated analyses like ARIMA, in order to develop an understanding of the basics.

FYI, 90 observations was a number picked at random.

I agree that Excel is not the ultimate tool. I already ordered a couple of books about R. Again, I am first trying to grasp the basics.

Doctor T