Lecture24

Lecture24 - 4/20/2011 Estimating the slope A point estimate...

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4/20/2011 1 STAT 350 Lecture 24 11.2 Inferences about the slope β Estimating the slope β A point estimate of β is b ˆ b S xy S xx x i y i 1 n ( x i )( y i ) x i 2 1 n ( x i ) 2 11.2 Inferences about the slope β Notation: β : the slope of the population regression line b: the slope of the sample regression line b is a point estimate of β , just like is a point estimate of μ p is a point estimate of π Goal: Statistical Inference A Confidence Intervals for β Testing Hypotheses about β x Sampling distribution of the slope b b follows a normal distribution Standardize b: xx b b S ) 1 , 0 ( ~ N s b b xx b Sampling distribution of the slope, b Standard Z distribution when σ is known: When σ is unknow, replacing σ b by s b gives us a familiar t distribution with df = n 2 b b b s xx ~ N (0,1) b s b b s e s xx b MSE s xx ~ t ( df n 2) Confidence interval for β The confidence interval for β is: b ± (t crit)s b Procedures: Calculate estimates b and s b Determine confidence level Find t crit from the table Interpret the interval for the true slope β b s b ~ t , df n 2
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4/20/2011 2 Example 11.4 (same data as 11.2) Calculate 95% CI for β : b ± (t crit)s b Step 1: Calculate b n 15 x i 218.1 y i 1693.6 x i 2 3577.01 x i y i 24252.54 y i 2 191672.90 b S xy S xx x i y i 1 n ( x i )( y i )
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Lecture24 - 4/20/2011 Estimating the slope A point estimate...

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