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Unformatted text preview: Regression
•! Predicts Y from X •! Linear regression assumes that the relationship between X and Y can be described by a line Correlation vs. regression Regression assumes...
•! Random sample •! Y is normally distributed with equal variance for all values of X The parameters of linear regression Y=! + X Positive ! ! =0 Estimating a regression line Y=a+bX
Higher Negative ! Lower Nomenclature
Residual: Finding the "least squares" regression line
ˆ Yi ! Yi
n i =1 Minimize: SSresidual = (Y ! Yˆ )
i i 2 Best estimate of the slope
n Remember the shortcuts:
XY # & " i" i "( X i ! X )(Yi ! Y ) = %" X iYi ( ! n % ( i =1 $ '
n b= i =1 (X
n i ! X )(Yi ! Y ) i =1 (X i ! X) 2 (= "Sum of cross products" over "Sum of squares of X") "( X
i =1 n i ! X ) = " Xi 2
2 () # &2 %" X i ( % ( $ ' ! n Finding a Example: Predicting age based on radioactivity in teeth
Many above ground nuclear bomb tests in the ‘50s and ’60s may have left a radioactive signal in developing teeth. Is it possible to predict a person’s age based on dental C14? Y = a + bX
So.. a = Y ! bX Teeth data:
Estimated
1963 1963 1965 1967 1969 1970 1973 1974 1980 1982 Teeth data:
Actual
1985 1986 1987 1989 1991 1991 1991 1951 1951 1958 Actual
1963 1964 1964 1970 1972 1973 1972 1975 1983 1983 Estimated
1982 1985 1987 1990 1991 1991 1992 1954 1956 1954 Let X be the estimated age, and Y be the actual age. ! X = 39488, ! Y = 39499 !X !Y
2 = 77968254, = 78011881 ! ( XY ) = 77990016 2 n = 20 X = 1974.40 Y = 1974.95 # & " ( X i ! X )(Yi ! Y ) = % " X iYi( ! $ ' i =1
n " X "Y
i i a = 1974.95 – (1.0139)(...
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This note was uploaded on 04/16/2010 for the course MATHEMATIC 1231 taught by Professor Driscoll during the Spring '10 term at Clayton College of Natural Health.
 Spring '10
 Driscoll
 Statistics, Correlation, Linear Regression, Variance

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