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lect3_103_2010_Compatibility_Mode_

# lect3_103_2010_Compatibility_Mode_ - Confidence Intervals I...

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4/5/2010 1 Confidence Intervals - I The last topic in our “Review of Statistics” is Confidence Intervals . Recall that we have an estimate, Y , of μ Y . Again, Y will likely be fairly close to μ Y, , but it will generally not equal μ Y . Given our estimate Y , we might want to try to quantify the range that μ Y might be in. We can do this using Confidence Intervals. Confidence Intervals - II Given our estimate Y , a 95% confidence interval for μ Y is given by: Statistically, this interval will contain (or “cover”) the true population mean μ Y 95% of the time. Hence, we can say that we are 95% confident that μ Y is in this interval or region. Confidence intervals are a very useful and intuitive way of describing what we have learned statistically. 2 2 1.96 , 1.96 Y Y s s Y Y n n - +

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4/5/2010 2 Confidence Intervals - III • Example: Suppose Y= 84, s 2 Y is 100, and n = 25. A 95% confidence interval for μ Y is: We would conclude that we are 95% sure that μ Y is in this range. ( ( 29 100 100 84 1.96 , 84 1.96 25 25 80.08 , 87.92 - + = Confidence Intervals - IV Notes: 1) Confidence interval shrinks (i.e. one gets a more precise interval) as: n increases (all else equal) s 2 Y decreases (all else equal) 2) Can also do 90% or 99% confidence intervals: 90% CI: 99% CI: To be more confident that your interval covers μ Y , you need a bigger interval! 2 2 1.64 , 1.64 Y Y s s Y Y n n - + 2 2 2.58 , 2.58 Y Y s s Y Y n n - +
4/5/2010 3 Linear Regression - I We now move to studying the “Linear Regression Model with One Regressor”.

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lect3_103_2010_Compatibility_Mode_ - Confidence Intervals I...

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