Linear Correlation: Is Evidence Sufficient?

• MHB
• Gigi1
In summary, the problem involves constructing a scatterplot and finding the linear correlation coefficient (r) and P-value for the given data. The significance level of alpha is 0.01 and the question asks if there is sufficient evidence to support a claim of linear correlation between the number of internet users and scientific award winners per capita.
Gigi1
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

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?

1. What is linear correlation?

Linear correlation is a statistical measure that describes the strength and direction of a relationship between two continuous variables. It is often represented by a correlation coefficient, with values ranging from -1 to 1.

2. How is linear correlation calculated?

To calculate linear correlation, we use a formula called the Pearson correlation coefficient, which measures the degree of linear relationship between two variables. This involves calculating the covariance and standard deviations of the two variables.

3. What does a correlation coefficient of 0 mean?

A correlation coefficient of 0 means that there is no linear relationship between the two variables. This does not necessarily mean that there is no relationship at all, as there could be a non-linear relationship or other factors at play.

4. Is a high correlation coefficient always a good thing?

Not necessarily. A high correlation coefficient means that there is a strong linear relationship between the two variables, but it does not necessarily imply causation. It is important to consider other factors and conduct further analysis before making any conclusions.

5. How do I determine if the evidence for linear correlation is sufficient?

The sufficiency of evidence for linear correlation depends on the context and the purpose of the analysis. Generally, a correlation coefficient closer to 1 or -1 indicates a stronger relationship, while a p-value less than 0.05 suggests that the correlation is statistically significant. However, it is important to also consider the sample size and potential confounding variables before making any conclusions.