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9 samples pairs of quantitative measurements

EXERCISE 1 – FATMINK. 1. DATA. acid digest otherfats 1 29.8 67.5 70.2 2 30.3 70.6 69.7 3 22.6 72.0 77.4 4 18.7 78.2 81.3 5 14.8 87.0 85.2 6 4.1 89.9 95.9 7 4.4 91.2 95.6

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9 samples pairs of quantitative measurements

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  1. EXERCISE 1 – FATMINK 1. DATA acid digest otherfats 1 29.8 67.5 70.2 2 30.3 70.6 69.7 3 22.6 72.0 77.4 4 18.7 78.2 81.3 5 14.8 87.0 85.2 6 4.1 89.9 95.9 7 4.4 91.2 95.6 8 2.8 93.1 97.2 9 3.8 96.7 96.2 • 9 samples • pairs of quantitative measurements • digestability seems to be dependent on the stearic acid content fatmink<-read.table(file.choose(),header=T) fatmink$otherfats<-with(fatmink,100-acid)

  2. 2. SCATTER PLOT • a scatter-plot for the distribution of the measurements • fitting the data with a linear model • calculating the intercept and the slope • plotting the regression line to the data plot(digest~otherfats,data=fatmink) fit.hypothesis<-lm(digest~otherfats,data=fatmink) coef(fit.hypothesis) intercept=3.1592033, slope=0.9337416 abline(coef(fit.hypothesis))

  3. 3. REGRESSION LINE FOR OTHER FATS Parameter1 = interception with y = 0 No other fats than stearic acid = no digestibility 0 + Parameter 2*100 = 100 When there are only other fats = full digestibility Parameter 2 =1 > y = 0 + 1 * x

  4. 4. ESTIMATED LINEAR RELATIONSHIP BETWEEN DIGESTION AND OTHER FATS fit.hypothesis<-lm(digest~otherfats,data=fatmink) fit.hypothesis2<-lm(digest~-1,offset=otherfats,data=fatmink) anova(fit.hypothesis,fit.hypothesis2) Model 1: digest ~ otherfats Model 2: digest ~ -1 Res.Df RSS Df Sum of Sq F Pr(>F) 1 7 61.764 2 9 122.530 -2 -60.766 3.4434 0.09094 . • creating a second linear model to be tested against the initial model • the models are similar

  5. 5. PREDICTING DIGESTION LEVELS FOR GIVEN VALUES OF OTHER FATS • model based expected values and their confidence intervals • With low otherfats i.e. high stearic acids there is low digestibility and vice versa predict(fit.hypothesis,new=data.frame(otherfats=0),interval="confidence") fit lwr upr 1 3.159203 -15.6929 22.01131 predict(fit.hypothesis,new=data.frame(otherfats=100),interval="confidence") fit lwr upr 1 96.53336 92.5722 100.4945

  6. 6. CHECKING THE INITIAL MODEL par(mfrow=c(1,2)) plot(fit,which=1:2) • with an adequate model the residuals should be evenly scattered around 0 • and the QQ-plot should look linear • better resolution with bigger sample size

  7. 7. SUMMARY Statistical methods Digestion is modelled by a simple linear regression with other fats as regressor. The effect of other fats is assessed by an F-test using a pre-specified significance level of 5%. The estimated levels of digestion are accompanied by 95% confidence intervals in parentheses. All analyses were made using R version 2.13.0 (www.r-project.org). Results The expected digestion with no stearic acid in the fat was estimated to 97% (92%-100,5%) and thus full digestion of fat with no stearic acid is supported by the data. Furthermore the expected digestion of fat consisting of only stearic acid is estimated to 3,2% (-15,7%-22,0%) and thus our data supports the claim that fat consisting only of stearic acid is non-digestible and the rest of the fat is fully digestable. Figure 1:Scatter-plot of digestion and stearic acid. The line is fitted by linear regression

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