Introductory Applied Statistics for the Life Sciences
Introductory Applied Statistics for the Life Sciences STAT 371
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This 2 page Class Notes was uploaded by Mrs. Triston Collier on Thursday September 17, 2015. The Class Notes belongs to STAT 371 at University of Wisconsin - Madison taught by Quoc Tran in Fall. Since its upload, it has received 25 views. For similar materials see /class/205074/stat-371-university-of-wisconsin-madison in Statistics at University of Wisconsin - Madison.
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Date Created: 09/17/15
Quoc Tran B248D MSC tran statwiscedu STAT 371 Discussion 11 May 5 2008 1 Linear Regression a Simple Linear Regression 0 Any line we can use to predict Y from X will have the form Y be le where be is the intercept and b1 will be the slope 2 96 W917 7i 2 96 W intercept b0 y 7 bli Slope b1 b0 and b1 are the estimates of 60 and 61 respectively7 in the following linear model Mylx 50 51X where MY X is the population mean Y value for a given X o The value qj be ha is the predicted value of Y if the explanatory variable X x For each data point xi77 the residual is the difference between the observed value and the predicted value7 yi 7 y Simple linear regression identi es the line that minimizes the residual sum of squares7 7 fl2 b Residual Standard Deviation The residual standard deviation7 SY X7 is a measure of a typical size of a residual It tells how far above or below the regression line points tend to be lts formula is SSresz39d 5YlX n 7 2 Within the framework of the linear model and the random subsampling model7 SY X is an estimate of UY X lnference Standard error of b1 is A O V Sylx 2 xi 7 i 95 con dence interval for 61 is b1 i 17025SE171 with degree of freedom for t is n 7 2 SE51 Correlation A CL V o The correlation coef cient r is the measure ofthe strength of the linear relationship between two variables7 on a scale from 1 to 1 Z 96139 W917 7i 2 96139 i i Z in 7 7i 0 The correlation coef cient is 71 or 1 only when the data lies perfectly on a line with negative or positive slope7 respectively 7 Of ce hours Mon Tue 400 500pm 1 httpwwwstatwiscedutran Quoc Tran B248D MSC tran statwiscedu o If the correlation coef cient is near 17 this means that the data is tightly clustered around a line with a positive slope 0 Correlation coef cients near 0 indicate weak linear relationships 0 Alternative formula correlation coef cient7 r is the square root of coef cient of determination7 r2 with sign of the slope of the regression line 0 Approximate relation of r to SY X and 8y V17 r2 N Lle 8Y 2 Examples Example 1 126 on page 539 Example 2 R solution for 126 lnterpret the output of R gt Xc003366101020203030 gt Yc33331029827828029025523818315511710 gt fitlmYX gt summary fit Call lmformula Y X Coefficients Estimate Std Error t value Prgtt Intercept 3182979 055693 5715 653e14 X 071201 003589 1984 232e 09 Signif codes 0 0001 001 005 01 1 Residual standard error 1295 on 10 degrees of freedom Multiple R Squared 09752 Adjusted R squared 09727 F statistic 3936 on 1 and 10 DF p value 2321e 09 gt anovafit Analysis of Variance Table Response Y Df Sum Sq Mean Sq F value PrgtF 1 66057 66057 39364 2321e 09 1678 168 X Residuals 10 Example 3 1223 on page 553 Construct a 95 con dence interval for the slope of the regression line in the previous example Of ce hours Mon Tue 400 500pm 2 httpwwwstatwiscedutran
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