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:

$$\begin{array}{c|cccccccccccccccccccccccccccccccccccc}X&95.42&95.88&93.05&94.58&98.22&99.65&98.75&100.21&97.02&96.48&95.85&97.44&95.66&96.99&94.71&98.66&95.32&95.00&90.65&88.41&87.02&86.05&82.78&81.52&79.81&80.40&79.53&80.25&79.72&81.40&80.19&80.66&80.26&80.32&82.14&81.54\\Y&48.91&49.10&45.92&38.34&33.75&33.62&37.04&41.65&46.59&45.09&49.20&47.12&59.47&60.30&59.63&47.60&49.76&48.24&53.27&66.15&80.54&91.16&95.96&98.17&105.37&102.71&99.74&101.58&102.59&97.49&98.42&92.72&96.38&102.33&107.65&105.03\end{array}$$

The equation of the regression line is:

$$y~=~369.8 ~-~ 3.344 \cdot x$$

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
95.66 59.47 5688.9002 9150.8356
96.99 60.30 5848.497 9407.0601
94.71 59.63 5647.5573 8969.9841
98.66 47.60 4696.216 9733.7956
95.32 49.76 4743.1232 9085.9024
95.00 48.24 4582.8 9025
90.65 53.27 4828.9255 8217.4225
88.41 66.15 5848.3215 7816.3281
87.02 80.54 7008.5908 7572.4804
86.05 91.16 7844.318 7404.6025
82.78 95.96 7943.5688 6852.5284
81.52 98.17 8002.8184 6645.5104
79.81 105.37 8409.5797 6369.6361
80.40 102.71 8257.884 6464.16
79.53 99.74 7932.3222 6325.0209
80.25 101.58 8151.795 6440.0625
79.72 102.59 8178.4748 6355.2784
81.40 97.49 7935.686 6625.96
80.19 98.42 7892.2998 6430.4361
80.66 92.72 7478.7952 6506.0356
80.26 96.38 7735.4588 6441.6676
80.32 102.33 8219.1456 6451.3024
82.14 107.65 8842.371 6746.9796
81.54 105.03 8564.1462 6648.7716

Step 2: Find the sum of every column:

$$ \sum{X} = 3221.54 ~,~ \sum{Y} = 2538.59 ~,~ \sum{X \cdot Y} = 220229.5907 ~,~ \sum{X^2} = 290362.335 $$

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

$$ \begin{aligned} a &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 2538.59 \cdot 290362.335 - 3221.54 \cdot 220229.5907}{ 36 \cdot 290362.335 - 3221.54^2} \approx 369.8 \\ \\b &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 36 \cdot 220229.5907 - 3221.54 \cdot 2538.59 }{ 36 \cdot 290362.335 - \left( 3221.54 \right)^2} \approx -3.344\end{aligned}$$

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

$$ \begin{aligned} y~&=~a ~+~ b \cdot x \\y~&=~369.8 ~-~ 3.344 \cdot x\end{aligned}$$

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Script name : correlation-and-regression-calculator

Form values: 95.42,95.88,93.05,94.58,98.22,99.65,98.75,100.21,97.02,96.48,95.85,97.44,95.66,96.99,94.71,98.66,95.32,95.00,90.65,88.41,87.02,86.05,82.78,81.52,79.81,80.40,79.53,80.25,79.72,81.40,80.19,80.66,80.26,80.32,82.14,81.54 , 48.91,49.10,45.92,38.34,33.75,33.62,37.04,41.65,46.59,45.09,49.20,47.12,59.47,60.30,59.63,47.60,49.76,48.24,53.27,66.15,80.54,91.16,95.96,98.17,105.37,102.71,99.74,101.58,102.59,97.49,98.42,92.72,96.38,102.33,107.65,105.03 , 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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