MHB Linear Correlation: Is Evidence Sufficient?

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SUMMARY

The discussion focuses on determining the linear correlation between the number of Internet users per 100 people and the number of scientific award winners per 10 million people across various countries. Participants are tasked with constructing a scatterplot, calculating the linear correlation coefficient (r), and finding the P-value of r using a significance level of alpha = 0.01. The analysis aims to establish whether sufficient evidence exists to support a claim of linear correlation between these two variables.

PREREQUISITES
  • Understanding of scatterplot construction
  • Knowledge of linear correlation coefficient (r)
  • Familiarity with P-value calculation
  • Basic statistics concepts, including significance levels
NEXT STEPS
  • Learn how to create scatterplots using tools like Excel or Python's Matplotlib
  • Study the calculation and interpretation of the linear correlation coefficient (r)
  • Explore hypothesis testing and P-value significance in statistical analysis
  • Investigate the implications of correlation versus causation in data analysis
USEFUL FOR

Statisticians, data analysts, students in statistics courses, and anyone interested in understanding the relationship between Internet usage and scientific achievement.

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The accompanying table lists the numbers of Internet users per 100 people and numbers of scientific award winners per 10 million people for different countries. Construct a​ scatterplot, find the value of the linear correlation coefficient​ r, and find the​ P-value of r. Determine whether there is sufficient evidence to support a claim of linear correlation between the two variables. Use a significance level of alpha = 0.01.

Internet users per 100 data, Award winners per 10 million data:
78.2, 5.4
83.0, 23.5
82.0, 8.7
40.1, 0.5
79.7, 5.0
38.9, 0.2
90.6, 23.8
93.7, 8.3
80.7, 10.4
84.3, 11.2
52.3, 3.2
81.2, 13.2
58.1, 2.4
76.4, 1.3
95.4, 10.8
97.5, 24.8
66.4, 2.0
54.7, 2.8
69.9, 2.9
97.7, 30.6
87.5, 31.7
83.6, 19.4
82.2, 9.9
 
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What was your purpose in posting this? Do you just want someone to do your homework for you?

The problem asks you to construct a "scatter plot". Do you know what a "scatter plot" is? Do you know what a "linear correlation coefficient​" and "P-value" are?
 
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