Chpt03

# Chpt03 - Chapter 3 Bivariate and Multivariate Data and...

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Chapter 3 Bivariate and Multivariate Data and Distributions Section 3.1 1. (a) The following stem-and-leaf displays were created by Minitab: Stem-and-leaf of temp N = 24 Leaf Unit = 1.0 1 17 0 3 17 23 6 17 445 8 17 67 8 17 (7) 18 0000011 9 18 2222 5 18 445 2 18 6 1 18 8 Each stem is repeated 5 times: the first stem of 17 has leaves of 0 and 1, the next stem has leaves 2 and 3, and so forth. 180 appears to be a typical value for this data. The distribution is reasonably symmetric in appearance and somewhat bell-shaped. The variation in the data is fairly small since the range of the values (188-170 = 18) is fairly small compared to the typical value of 180. Stem-and-leaf of ratio N = 24 Leaf Unit = 0.10 3 0 889 7 1 0000 8 1 3 12 1 4444 12 1 66 10 1 8889 6 2 11 4 2 4 2 5 3 2 6 2 2 2 3 00 For the 'ratio' data, a typical value is around 1.6 and the distribution appears positively skewed. The hundredths digit has been truncated in the display. The variation in the data is large since the range of the data (3.08 - .84 = 2.24) is very large compared to the typical value of 1.6. The two largest values could be outliers and should be checked using the methods of Section 2.3. (b) The efficiency ratio is not uniquely determined by temperature since there are several instances in the data of equal temperatures associated with different efficiency ratios. For example, the five observations with temperatures of 180 each have different efficiency ratios. (c) A scatter plot of the data appears below. The points exhibit quite a bit of variation and do not appear to fall close to any straight line or simple curve. 3 2 Efficiency ratio

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Chapter 3 Bivariate and Multivariate Data and Distributions 2 2. 15 10 5 0 5 4 3 2 1 0 age emissions for baseline 15 10 5 0 7 6 5 4 3 2 1 0 age emissions for reformulated With this data the relationship between the age of the lawn mower and its NO x emissions seems somewhat dubious. One might have expected to see that as the age of the lawn mower increased the emissions would also increase. We certainly do not see such a pattern. Age does not seem to be a particularly useful predictor of NO x emission. 3. A scatter plot of the data appears below. The points fall very close to a straight line with an intercept of approximately 0 and a slope of about 1. This suggests that the two methods are producing substantially the same concentration measurements. Concentration (sensor method) 220
Chapter 3 Bivariate and Multivariate Data and Distributions 3 4. (a) 150 100 50 0 BOD mass loading 90 80 70 60 50 40 30 20 10 0 BOD mass removal On both the BOD mass loading boxplot and the BOD mass removal boxplot there are 2 outliers. Both variables are positively skewed.

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Chapter 3 Bivariate and Multivariate Data and Distributions 4 (b) 150 100 50 0 90 80 70 60 50 40 30 20 10 0 BOD mass loading BOD mass removal There is a strong linear relationship between BOD mass loading and BOD mass removal. As the BOD mass loading increases so does the BOD mass removal. The two outliers seen on each of the boxplots are seen to be correlated here. There is one observation that appears not to match the linear pattern.
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Chpt03 - Chapter 3 Bivariate and Multivariate Data and...

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