Showing Revision 5 created 05/25/2016 by Udacity Robot.

1. Title:
   Confidence Intervals - Intro to Inferential Statistics
2. Description:

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   Although using the standard error of the estimate can help us assess the
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   accuracy of our predictions. We can make even more accurate predictions by
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   computing confidence intervals for our predicted values, our y-hats. In other
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   words, when we get our regression line, we have our expected value which is
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   this y-hat naught, for a specified value x-naught. However, the actual value
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   might be anything from up here, to down here, or it might be exactly equal to
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   our predicted value. Therefore, we might want a confidence interval around our
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    expected value for where the actual value might be. Similarly, we might want a
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    confidence interval for the true slope. We'll have a certain regression line
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    and we'll have calculated the slope for that regression line based on our
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    sample data. And this is just an example, the slope could be this, or flatter
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    down to here. A confidence interval for a slope can tell us the range for which
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    the true population's slope might be. You won't actually calculate the
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    confidence interval in this lesson, because we're going to assume that you'll
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    use a computer to get it. The important thing is that you know what it means.
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    For example, let's say we have some sample data that looks like this. We
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    calculate that the regression line is y equals bx plus a. Some slope and some
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    intercept. But lets say then that we're able to look at all the population
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    data. And it looks like this. Now it looks to be slightly downward sloping.
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    Since we're assuming this is the true regression line, we'll use the common
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    notation for the regression coefficients for the population. Oh, and these
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    should have hats since they're the predicted values. If this were the case,
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    where the sample regression line is positively sloping. But the true regression
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    line for the population is negatively sloping. That would mean that the
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    confidence interval for b has a negative lower bound and a positive upper
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    bound. It includes zero within this range. Therefore, if we run a two-tailed
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    hypothesis test for whether or not the slope is equal to zero. We would fail to
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    reject the null, meaning there's no evidence that there's a linear relationship
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    between x and y based on that sample. In fact, let's get more into hypothesis
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    testing for slope.