Correlation and regression calculator

Enter two data sets and this calculator will find the equation of the regression line and corelation coefficient. The calculator will generate a step by step explanation along with the graphic representation of the data sets and regression line.

Result:

You entered the following data:

$$\begin{array}{c|cccccccccccc}X&48.91&49.10&45.92&38.34&33.75&33.62&37.04&41.65&46.59&45.09&49.20&47.12\\Y&95.42&95.88&93.05&94.58&98.22&99.65&98.75&100.21&97.02&96.48&95.85&97.44\end{array}$$

The equation of the regression line is:

$$y~=~105.1 ~-~ 0.1908 \cdot x$$

The graph of the regression line is:

Explanation:

We will find an equation of the regression line in 4 steps.

Step 1: Find $X \cdot Y$ and $X^2$ as it was done in the table below.

$X$$Y$$X\cdot Y$$X \cdot X$ 
48.91 95.42 4666.9922 2392.1881
49.10 95.88 4707.708 2410.81
45.92 93.05 4272.856 2108.6464
38.34 94.58 3626.1972 1469.9556
33.75 98.22 3314.925 1139.0625
33.62 99.65 3350.233 1130.3044
37.04 98.75 3657.7 1371.9616
41.65 100.21 4173.7465 1734.7225
46.59 97.02 4520.1618 2170.6281
45.09 96.48 4350.2832 2033.1081
49.20 95.85 4715.82 2420.64
47.12 97.44 4591.3728 2220.2944

Step 2: Find the sum of every column:

$$ \sum{X} = 516.33 ~,~ \sum{Y} = 1162.55 ~,~ \sum{X \cdot Y} = 49947.9957 ~,~ \sum{X^2} = 22602.3217 $$

Step 3: Use the following equations to find $a$ and $b$:

$$ \begin{aligned} a &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 1162.55 \cdot 22602.3217 - 516.33 \cdot 49947.9957}{ 12 \cdot 22602.3217 - 516.33^2} \approx 105.1 \\ \\b &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 12 \cdot 49947.9957 - 516.33 \cdot 1162.55 }{ 12 \cdot 22602.3217 - \left( 516.33 \right)^2} \approx -0.1908\end{aligned}$$

Step 4: Substitute $a$ and $b$ in regression equation formula

$$ \begin{aligned} y~&=~a ~+~ b \cdot x \\y~&=~105.1 ~-~ 0.1908 \cdot x\end{aligned}$$

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Script name : correlation-and-regression-calculator

Form values: 48.91,49.10,45.92,38.34,33.75,33.62,37.04,41.65,46.59,45.09,49.20,47.12 , 95.42,95.88,93.05,94.58,98.22,99.65,98.75,100.21,97.02,96.48,95.85,97.44 , reg

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Correlation and Regression Calculator
Input X and Y values separated by comma or blank space
show help ↓↓ examples ↓↓
Use data grit to input x and y values
Find the equation of the regression line
Find the corelation coefficient
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examples
example 1:ex 1:

Consider the following set of points: ${(-3 , -4), \, (2 , 3), \, (7 , 11)}$

a) Find the regression line for the given data points.

b) Plot the given points and the regression line.

example 2:ex 2:

The values of $X$ and their corresponding values of $Y$ are shown in the table below:

$$ \begin{array}{c|ccccc} X & ~1~ & ~2~ & ~3~ & ~4~ & ~5 \\ Y & ~4~ & ~8~ & ~9~ & ~11~& ~16 \end{array} $$

Find a Pearson correlation coefficient.

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