203ch6_slides.pdf - STAT 203 Chapter 6 Scatterplots...

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STAT 203 Chapter 6 Scatterplots, Association, and Correlation Motivating Examples Question #1: Do people with bigger brains tend to be more intelligent? Statistical process of investigation: 1. Formulate research question: How is human intelligence related to the brain size? Does brain size predict intelligence in humans? 2. Collect data: What variables to collect (how to measure brain size and intelligence)? Who do we collect data on? Eugenia Yu, UBC Department of Statistics. Not to be copied, used, or revised without explicit written permission from the copyright owner. 1
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STAT 203 3. Examine the data: How do we explore the relationship between brain size and intelligence? We will learn the techniques in this chapter. 4. Interpret the results and draw conclusions Eugenia Yu, UBC Department of Statistics. Not to be copied, used, or revised without explicit written permission from the copyright owner. 2
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STAT 203 Question #2: Does skipping classes jeopardize academic performance in a course? Statistical process of investigation: 1. Formulate research question: How is academic performance related to class skipping (or attendance)? 2. Collect data: What variables to collect (how to measure class skipping and academic performance)? Who do we collect data on? 3. Examine the data: How do we explore the relationship between amount of classes skipped and academic performance? 4. Interpret the results and draw conclusions Eugenia Yu, UBC Department of Statistics. Not to be copied, used, or revised without explicit written permission from the copyright owner. 3
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STAT 203 Solution to Question #1: How is human intelligence related to the brain size? We will measure intelligence by IQ and brain size by the pixel count of gray scale in MRI brain scan images. Suppose we collect data on 10 individuals: Person MRI count IQ 1 816932 124 2 951545 122 3 991305 135 4 833868 114 5 856472 125 6 852244 113 7 790619 121 8 866662 116 9 857782 129 10 948066 105 Note that both IQ and MRI count are quantitative variables! Eugenia Yu, UBC Department of Statistics. Not to be copied, used, or revised without explicit written permission from the copyright owner. 4
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STAT 203 Scatterplots help visualize possible relationship between two quantitative (but not categorical) variables a plot of pairs of observations on the x - y plane, e.g., x i = MRI count for person i , y i = IQ for person i the mean-mean point ( x, y ) provides the center of the cloud of data points: e.g., x = 876549 . 5 , y = 120 . 4 Eugenia Yu, UBC Department of Statistics. Not to be copied, used, or revised without explicit written permission from the copyright owner. 5
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  • Winter '18
  • EugeniaHoiYinYu
  • Pearson product-moment correlation coefficient, Spearman's rank correlation coefficient, Eugenia Yu, UBC Department of Statistics

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