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Chapter00 - Initial Data Exploration STAT 563 Spring 2007...

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Initial Data Exploration STAT 563 Spring 2007 Mani Lakshminarayanan

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Inheritance of Height Original data collected by E.S. Pearson during 1893-1898 n=1375 heights of mothers under the age of 65 and one of their adult daughters over the age of 18 Questions: Do taller mothers tend to have taller daughters? Do shorter mothers tend to have shorter daughters?
dat1 <- read.table("C:/My Documents/heights.txt",header=TRUE) plot(Mheight,Dheight) mhround <- round(Mheight,0) dat3 <- data.frame(mhround,Dheight) xsub <- dat3[mhround %in% c(58,64,68),] plot(xsub\$mhround,xsub\$Dheight)

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Height Data
Observations The range of data appear to be the same for both mothers and daughters To avoid over plotting, one could use jittering (add a small perturbation to each data points) Response variable seems to depend on the predictor variable ( mothers height) Next plot shows that there is an increasing trend Variability is approximately the same for each mother- daughter pair slices Scatter appears to be elliptically shaped with an increasing trend None of the points appear to be different from the cluster ( outliers)

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Height Data

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Forbes Data
Forbes Data

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Observation Number of observations small All points appear to fall on a smoothed curve (ie, variability in pressure for a given temperature is small) Though most points appear to fall on the line, there appears to be a systematic trend (systematic error), those in the middle fall below the line and the highest and lowest fall above the line (except for one point) This is much easier to see in the plot on the side where residual =pressure-point on the line is plotted To get the same resolution in the first plot, we need 10/0.8 = 12.5 as big as the second one
Observation Though there is nothing wrong with the curvature (non-linear), most of the theory to be discussed in this course is suited best if the fit is a straight line Transformation of one or both variables could help to get linearity Forbes used a logarithmic scale Straight line appears to be reasonable There appears to be no systematic deviation from the straight line

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Forbes Data
Forbes Data

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Old Faithful Geyser, Yellowstone Park

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Characteristics Data look bi-modal with two clusters Common mean is not a good measure of location as there are two peaks, around 2 and 4.5 Standard deviation may not be a good measure of spread No obvious outliers Two clusters Granularity (not rounded to one decimal place) might give a better picture

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Some Typical Plots
No relationship

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Strong Linear (Positive Correlation)
Strong Linear (Negative Correlation)

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Exact Linear (Positive Correlation)

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Chapter00 - Initial Data Exploration STAT 563 Spring 2007...

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