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Unformatted text preview: _____________________________________________________ Use the LinRegTTest option in your calculator to conduct a test of hypothesis at the = 0.05 significance level whether true mean female Vipera bertis weight tends to increase with increase in female Vipera bertis length. Regression and Correlation Page 10 Coefficient of Determination (r2) Recall SS(resid) is a measure of the unexplained variablility in Y (the variation in Y not explained by X through the regression model) and is given by n SS resid SSE yi ‐yi 2 Scatterplot of W
eight vs Length i1 with Fitted Regression Line
200 Definition: SS(total) measures the total variability in Y and is given by Weight (g) n yi ‐y 2 SS total SST 180 i1 160
120 Definition: SS(reg) measures the variability in Y that is explained by X through the regression model and is given by 100 55.0 57.5 60.0
) 65.0 67.5 70.0 n yi ‐y 2 SS reg SSR i1 Then, SS(total) = SS(reg) + SS(resid) or the total variability in Y is explained by the regression model plus the unexplained residual variation. Definition: The coefficient of determination is the ratio between the SS(reg) and SS(total) and is given by ∑n 1 xi ‐x yi ‐y 2
i n coefficient of determination r ∑i 1 xi ‐x 2 ∑n 1 yi ‐y 2
2 and is interpreted as the proportion (or percentage) of variability in Y that is explained by the linear regression of Y on X. Find and interpret r2 for the regression of female Vipera bertis weight on length. Regression and Correlation Page 11 Reading Regression Output from Standard Statistical Software Example Fertility Enhancer Data The data below concerns the prevalence of a so called fertility enhancer and the population of Oldenburg Germany in thousands of people between 1930 and 1936. The original data set can be found in: Ornithologische Monatsberichte, 44, No.2, Jahrgang, 1936, Berlin and 48, No.1, Jahrang, 1940, Berlin, and Statistiches Jarbuch Deutscher Gemeinden, 27‐33, Jahrang, 1932‐1938, Gustav Fischer, Jena. The actual data below is estimated from the graph in Box, Hunter...
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This note was uploaded on 02/27/2013 for the course STAT 205 taught by Professor Hendrix during the Fall '09 term at South Carolina.
- Fall '09