How to Find Correlation Coefficient p value in R, linear relationship between two variables can be quantified using the Pearson correlation coefficient.

The value of this correlation coefficient is always between -1 and 1, where:

-1: A linear correlation between two variables that is perfectly negative

0: The pair of variables do not correlate linearly.

+1: The variables have a perfect positive linear connection with the other.

A correlation coefficient’s corresponding t-score and p-value can be computed to see if it is statistically significant.

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The correlation coefficient (r) t-score can be computed using the following formula:

t = r√n-2 / √1-r^{2}

The corresponding two-sided p-value for the t-distribution with n-2 degrees of freedom is used to determine the p-value.

You can use the cor.test() function in R to get the p-value for a Pearson correlation coefficient.

cor.test(x, y)

An example of how to utilize this function in real life is provided below.

## Example: Use R to get the P-Value for the correlation coefficient.

The code below demonstrates how to determine the p-value for the correlation coefficient between two variables in R using the cor.test() function:

x <- c(710, 718, 920, 817, 834, 886, 951, 474, 683, 485) y <- c(490, 594, 279, 286, 284, 283, 888, 392, 276, 275) #calculate correlation coefficient and corresponding p-value cor.test(x, y)

earson's product-moment correlation data: x and y t = 0.74819, df = 8, p-value = 0.4758 alternative hypothesis: true correlation is not equal to 0 95 percent confidence interval: -0.4456532 0.7625712 sample estimates: cor 0.2557295

From the output we can see:

The Pearson correlation coefficient is 0.2557295.

The corresponding p-value is 0.4758.

There is a positive linear relationship between the two variables, as indicated by the positive correlation coefficient.

Nevertheless, the association is not statistically significant because the p-value of the correlation coefficient is not less than 0.05.

To extract simply the p-value for the correlation coefficient, note that we may also enter cor.test(x, y)$p.value:

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