So, we have the some of the squares and we have the cross products.

Sample standard deviation

Std. deviation

Std dev.

Deviation

Std. dev

Standard deviation

standardDeviation

Standard Deviation

Let's now consider linear regressions of standard scores.

This is just simple algebra. So here's the formulas for Z, that's from

Expressed through standard deviation Values given over accidental errors.

A common measure of intelligence, IQ, is distributed with a mean of 100 and a standard deviation of 15.

Standard deviation of the distribution

STD is the standard deviation of the distribution.

Standard deviation of the normal distribution

We also applied it to 10,000 people. Our average loss in this case was 20 pounds.

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And they would come from time to time and check my blood level.

It is equal to the square root of the sum of the deviations in the y's over the deviations of the x's.

And sometimes it's easier to think in terms of sigma.

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This is no accident, somebody knew how to handle that stuff.

This is no accident.

We said it's 1, and so because it's not 1 it must be less than that.

It just moved over to the right by 5. If I were to try to make the standard deviation smaller we'll see that the whole thing just gets a little bit tighter.

As we know, this gives us an estimated mean.

Standard deviation for the total population

We add those up we get 250 and now we divide by 5 to get back our 50.

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So this is really considerable.

So this transformation shows that doubling the salary doubles the µ but also doubles the σ.

To see this, recall that as you just discovered b is equal to r times times the standard deviation of y over the standard deviation of x.

Can you guess what the effect is of adding 1000 to your salary on the mean and the standard deviation?

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Data structure. Mean.

Standard deviation of the standard logarithmic distribution

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And if you take its square root for the standard deviation, which is what we do right here, it's 0.49.

And I'll just call this, what's the probability that I land between 1 standard deviation the mean is minus 5 one standard deviation below the mean is minus 15 and one standard deviation above the mean is 10 plus minus 5 is 5.

Let me modify my question and let me say this time I expressed things in terms of standard deviations and not variances.

And now we get to the confidence interval.

If there's one thing you want to take home from this class that is that as you get more data as a statistician, your confidence increases so your confidence interval shrinks, whereas of course more data doesn't change the standard deviation.