Regression 1

# 24 february 2012 9 18 formula of course there is a

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Formula Of course, there is a formula for r , the sample correlation. r = 1 n - 1 n X i =1 x i - ¯ x s x y i - ¯ y s y We’ll work some example of this out later. Douglas Whitaker (Statistics Department) STA 3024: Regression 24 February 2012 10 / 18
The Regression Model When doing regression, we’re going to assume that each observation ( y i ) is generated (e.g. created by Mother Nature) according to a model. This model will change and get progressively more complicated over the next month. For simple linear regression, our model will be: y i = α + βx i + e i Douglas Whitaker (Statistics Department) STA 3024: Regression 24 February 2012 11 / 18

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The Simple Linear Regression Model y i = α + βx i + e i α represents the Y intercept β represents the slope of the line x i represents the value of the explanatory variable for datum i y i represents the value of the response variable for datum i e i represents the random error present for datum i (assumed to be normally distributed with a mean of 0 and a standard deviation of σ ) Douglas Whitaker (Statistics Department) STA 3024: Regression 24 February 2012 12 / 18
The Fitted Line We’re using Greek letters here because this represents the true, unknown model: y i = α + βx i + e i What we’re going to do is estimate the values of α and β from the data. ˆ y i = ˆ α + ˆ βx i The little hats mean these are estimates. Douglas Whitaker (Statistics Department) STA 3024: Regression 24 February 2012 13 / 18

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The Fitted Values ˆ y i = ˆ α + ˆ βx i Notice that we have an estimated value for y i . This estimated value, ˆ y i
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