# How to Use cor() to Calculate Correlation Coefficients in R

You can use the cor() function in R to calculate correlation coefficients between variables.

Here are the most common ways to use this function:

Method 1: Calculate Pearson Correlation Coefficient Between Two Variables

`cor(df\$x, df\$y)`

Use the Pearson correlation coefficient when calculating the correlation between two continuous variables. (e.g. height and weight)

Method 2: Calculate Pearson Correlation Coefficient Between All Numeric Variables in Data Frame

`cor(df)`

This method will return a correlation matrix that contains the Pearson correlation coefficient between each pairwise combination of numeric variables in a data frame.

Method 3: Calculate Spearman Correlation Coefficient Between Two Variables

`cor(df\$x, df\$y, method='spearman')`

Use the Spearman correlation coefficient when calculating the correlation between two ranked variables. (e.g. rank of a student’s math exam score vs. rank of their science exam score in a class)

Method 4: Calculate Kendall’s Correlation Coefficient Between Two Variables

`cor(df\$x, df\$y, method='kendall')`

Use the Kendall correlation coefficient when when you wish to use Spearman Correlation but the sample size is small and there are many tied ranks.

The following examples show how to use each method in practice with the following data frame in R that shows the number of hours spent studying, number of practice exams taken, and final exam score for eight different students:

```#create data frame
df <- data.frame(hours=c(1, 1, 3, 2, 4, 3, 5, 6),
prac_exams=c(4, 3, 3, 2, 3, 2, 1, 4),
score=c(69, 74, 74, 70, 89, 85, 99, 90))

#view data frame
df

hours prac_exams score
1     1          4    69
2     1          3    74
3     3          3    74
4     2          2    70
5     4          3    89
6     3          2    85
7     5          1    99
8     6          4    90
```

## Example 1: Calculate Pearson Correlation Coefficient Between Two Variables

The following code shows how to use the cor() function to calculate the Pearson correlation coefficient between the hours and score variables:

```#calculate Pearson correlation coefficient between hours and score
cor(df\$hours, df\$score)

 0.8600528
```

The Pearson correlation coefficient between hours and score turns out to be 0.86.

Note that if there are NA values in your data frame, you can use the argument use=’complete.obs’ to only use the rows where there are no NA values:

```#calculate Pearson correlation coefficient and ignore any rows with NA
cor(df\$hours, df\$score, use='complete.obs')```

## Example 2: Calculate Pearson Correlation Coefficient Between All Numeric Variables

The following code shows how to use the cor() function to create a correlation matrix that contains the Pearson correlation coefficient between all numeric variables in the data frame:

```#calculate Pearson correlation coefficient between all numeric variables
cor(df)

hours prac_exams      score
hours       1.0000000 -0.1336063  0.8600528
prac_exams -0.1336063  1.0000000 -0.3951028
score       0.8600528 -0.3951028  1.0000000
```

Here’s how to interpret the output:

• The Pearson correlation coefficient between hours and prac_exams is -.13.
• The Pearson correlation coefficient between hours and score is .86.
• The Pearson correlation coefficient between prac_exams and score is -.39.

Note: The Pearson correlation coefficient between each individual variable and itself is always 1, which is why each value along the diagonal of the correlation matrix is 1.

## Example 3: Calculate Spearman Correlation Coefficient Between Two Variables

The following code shows how to use the cor() function to calculate the Spearman correlation coefficient between the hours and prac_exams variables:

```#calculate Spearman correlation coefficient between hours and prac_exams
cor(df\$hours, df\$prac_exams, method='spearman')

 -0.1250391
```

The Spearman correlation coefficient between hours and prac_exams turns out to be -.125.

## Example 4: Calculate Kendall’s Correlation Coefficient Between Two Variables

The following code shows how to use the cor() function to calculate Kendall’s correlation coefficient between the hours and prac_exams variables:

```#calculate Kendall's correlation coefficient between hours and prac_exams
cor(df\$hours, df\$prac_exams, method='kendall')

 -0.1226791
```

Kendall’s correlation coefficient between hours and prac_exams turns out to be -.123.