# Find Linear Correlation Coefficient & P-Value for Internet Users & Award Winners

• MHB
• reaganlivi
In summary, the conversation discusses a student's difficulty with finding the test statistic for a scatter plot and linear correlation coefficient in a statistics class. The student has a chart with numbers of Internet users and scientific award winners for different countries and is seeking guidance on how to find the test statistic. They mention using a t-test to test for significance and mention the formula for calculating the t-value and degrees of freedom.
reaganlivi
Wooo! I am almost done with my stats class. I am having a reoccurring issue with finding the test statistic using a scatter plot and linear correlation coefficient.

Internet Users (Per 100) Award Winners (Per 10 Million)
78.2 5.5
79.5 9
55.8 3.3
67.2 1.6
76.9 10.9
39.1 0.1

I was given this chart above, I know how to put it into a scatter plot, as well as find the linear correlation coefficient. However, I am not positive on how to get the test statistic.

Listed below are 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 alphaequals 0.01.

Hi reaganlivi, welcome to MHB! ;)

Usually we do a t-test to test for significance of a linear regression to see if the slope is different from zero.
The t-value is the slope divided by the standard error of the slope.
And the degrees of freedom is n-2.

## 1. What is a linear correlation coefficient?

A linear correlation coefficient, also known as Pearson's correlation coefficient, is a measure of the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, with a value of 0 indicating no correlation and values closer to -1 or 1 indicating a stronger linear relationship.

## 2. Why is it important to find the linear correlation coefficient?

The linear correlation coefficient is important because it allows us to quantify the relationship between two variables. This can help us understand how changes in one variable may affect the other, and can be used to make predictions and identify patterns in data.

## 3. How is the linear correlation coefficient calculated?

The linear correlation coefficient is calculated by dividing the covariance of the two variables by the product of their standard deviations. The formula is r = (cov(X,Y) / (σX * σY), where r represents the correlation coefficient, cov represents the covariance, and σ represents the standard deviation of each variable.

## 4. What is a p-value and how is it related to the linear correlation coefficient?

A p-value is a measure of the probability that the observed correlation between two variables is due to chance. In other words, it tells us how likely it is that the observed relationship between the variables is not significant. The p-value is closely related to the linear correlation coefficient, as a higher correlation coefficient will result in a lower p-value, indicating a stronger relationship between the variables.

## 5. How can the linear correlation coefficient and p-value be used to interpret the relationship between internet users and award winners?

The linear correlation coefficient and p-value can be used to determine the strength and significance of the relationship between internet users and award winners. If the correlation coefficient is close to 1 and the p-value is low, this would indicate a strong positive relationship between the two variables, suggesting that as the number of internet users increases, the number of award winners also increases. If the correlation coefficient is close to 0 and the p-value is high, this would suggest that there is no significant relationship between the variables.