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Chapter 3
Descriptive Study of Bivariate
Data
Ananda Manage, PhD
Associate Professor of Statistics
Department of Mathematics and Statistics
Sam Houston State University
Figure, Temperature and Ozone P 85
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3.1 Summarization of Bivariate Categorical
Data
Table 1, Cross-Tabulated Frequency Counts, p. 86.
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Table 2, Relative Frequencies for the Data of Table 1, p. 87.
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Simpson’s Paradox
Table 3, Relative Frequencies by Group, p. 87.
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.
Does this appear to be a gender bias?
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Table 5, Admission Rates by Department, p. 88.
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3.3 Scatter Diagram of Bivariate
Measurement Data
Figure 1, Scatter diagram of applicants' scores, p. 94.
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Figure 2, Scatter
diagrams; A =
Lake Apopka; B =
Lake Woodruff, p.
95, 96.
Data, p. 95.
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3.4 The Correlation Coefficient
Box, Sample Correlation Coefficient, p. 98.
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Box, Calculation Formula for the Sample Correlation Coefficient, p. 99.
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Table 8, Calculation of r, p. 99.
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Table 9, Alternate Calculation of r, p. 100.
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An observed correlation between two variables may be spurious.
That is, it may be caused by the influence of a third variable.
Figure 4, r is not appropriate – samples from two populations, p. 101.
Correlation and Causation:- Spurious correlation can be caused
by lurking variables
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Figure 6, Scatter diagram pattern has strong relation to year, p. 102.
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Figure 8, Scatter diagrams (Problem 3.21), p. 105.
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Box, Lurking Variables, p. 103.
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Figure 9, Scatter diagram (Problem 3.22), p. 105.
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2.5 Linear Regression
Table 11, Data of Concentration x and Drying Time y (in minutes) and
the Basic Calculations, p. 109.
Figure 10, The line yˆ  ˆ  ˆ  , p. 108
0
1
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28
Coefficient of Determination r2
Fitted Line
The coefficient of determination r2 measures the goodness of fit
of the regression equation to the data. We interpret r2 as the
proportion of the variability in y that is accounted for by the linear
relationship between y and x. The values that r2 can take are 0 ≤ r2
≤ 1.
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Regression Example
STAT/MATH 3379
Weight of animals can be estimated using their heart girth. Following data set is from a sample
of six cows. Weights and heart girth are given in pounds and inches respectively.
Model Summary
Model
1
Cow
Weight
Heart Girth
1
641
214
2
633
215
3
651
216
4
666
217
5
688
219
6
680
221
R
.898a
R Square
.806
Adjusted R
Std. Error of the
Square
Estimate
.758
10.76225
a. Predictors: (Constant), HeartGirth
Coefficientsa
Standardized
(a)
(b)
(c)
(d)
(e)
Construct a scatterplot.
Find the correlation coefficient.
Find the regression line.
Interpret coefficient b.
Interpret coefficient of determination.
Unstandardized Coefficients
Model
1
B
Std. Error
(Constant)
-974.049
400.543
HeartGirth
7.529
1.846
Coefficients
Beta
t
.898
Sig.
-2.432
.072
4.079
.015
a. Dependent Variable: Weight
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