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103lect3hand - Confidence Intervals - I The last topic in...

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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. 22 1.96 , 1.96 YY ss nn ⎛⎞ −+ ⎜⎟ ⎝⎠ Confidence Intervals - III • Example: Suppose Y= 84, s 2 Y is 25, and n = 100. • A 95% confidence interval for μ Y is: • We would conclude that we are 95% sure that μ Y is in this range. () 100 100 84 1.96 , 84 1.96 25 25 80.08 , 87.92 =
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Confidence Intervals - IV •N o t e s : 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: –9 0 % C I : 9 % C I : To be more confident that your interval covers μ Y , you need a bigger interval! 22 1.64 , 1.64 YY ss nn ⎛⎞ −+ ⎜⎟ ⎝⎠ 2.58 2.58 Linear Regression - I • We now move to studying the “Linear Regression Model with One Regressor”. Regression models study the relationship between variables.
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This note was uploaded on 05/26/2008 for the course ECON 103 taught by Professor Sandrablack during the Spring '07 term at UCLA.

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103lect3hand - Confidence Intervals - I The last topic in...

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