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:

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

The equation of the regression line is:

$$y~=~189.5 ~-~ 1.512 \cdot x$$

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$ 
95.42 48.91 4666.9922 9104.9764
95.88 49.10 4707.708 9192.9744
93.05 45.92 4272.856 8658.3025
94.58 38.34 3626.1972 8945.3764
98.22 33.75 3314.925 9647.1684
99.65 33.62 3350.233 9930.1225
98.75 37.04 3657.7 9751.5625
100.21 41.65 4173.7465 10042.0441
97.02 46.59 4520.1618 9412.8804
96.48 45.09 4350.2832 9308.3904
95.85 49.20 4715.82 9187.2225
97.44 47.12 4591.3728 9494.5536

Step 2: Find the sum of every column:

$$ \sum{X} = 1162.55 ~,~ \sum{Y} = 516.33 ~,~ \sum{X \cdot Y} = 49947.9957 ~,~ \sum{X^2} = 112675.5741 $$

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

$$ \begin{aligned} a &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 516.33 \cdot 112675.5741 - 1162.55 \cdot 49947.9957}{ 12 \cdot 112675.5741 - 1162.55^2} \approx 189.5 \\ \\b &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 12 \cdot 49947.9957 - 1162.55 \cdot 516.33 }{ 12 \cdot 112675.5741 - \left( 1162.55 \right)^2} \approx -1.512\end{aligned}$$

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

$$ \begin{aligned} y~&=~a ~+~ b \cdot x \\y~&=~189.5 ~-~ 1.512 \cdot x\end{aligned}$$

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Script name : correlation-and-regression-calculator

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