# Probability of regression result

#### DrAnthonyRodriguez

##### New Member
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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#### staassis

##### Member
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
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.

#### DrAnthonyRodriguez

##### New Member
This is a hw problem ...
Dear Staassis,

It's not a HW problem; I am learning stats on my own.

I looked at CIs and PIs but I am looking for the 95% probability of a value higher than X, not the probability of a range.

Tony

#### staassis

##### Member
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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Dear Staassis,