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:

$$\begin{array}{c|cccccccccccccccccccccccccccccccccccc}X&95.42&95.88&93.05&94.58&98.22&99.65&98.75&100.21&97.02&96.48&95.85&97.44&95.66&96.99&94.71&98.66&95.32&95.00&90.65&88.41&87.02&86.05&82.78&81.52&79.81&80.40&79.53&80.25&79.72&81.40&80.19&80.66&80.26&80.32&82.14&81.54\\Y&1.1174&1.1311&1.1339&1.1099&1.1092&1.0859&1.0877&1.0736&1.1235&1.1221&1.1139&1.0995&1.1213&1.1149&1.0779&1.0837&1.1349&1.1621&1.2331&1.2472&1.2672&1.2901&1.3316&1.3539&1.3592&1.3732&1.3812&1.3822&1.3658&1.3610&1.3703&1.3492&1.3634&1.3347&1.3309&1.3080\end{array}$$

The equation of the regression line is:

$$y~=~2.578 ~-~ 0.01515 \cdot x$$

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 1.1174 106.622308 9104.9764
95.88 1.1311 108.449868 9192.9744
93.05 1.1339 105.509395 8658.3025
94.58 1.1099 104.974342 8945.3764
98.22 1.1092 108.945624 9647.1684
99.65 1.0859 108.209935 9930.1225
98.75 1.0877 107.410375 9751.5625
100.21 1.0736 107.585456 10042.0441
97.02 1.1235 109.00197 9412.8804
96.48 1.1221 108.260208 9308.3904
95.85 1.1139 106.767315 9187.2225
97.44 1.0995 107.13528 9494.5536
95.66 1.1213 107.263558 9150.8356
96.99 1.1149 108.134151 9407.0601
94.71 1.0779 102.087909 8969.9841
98.66 1.0837 106.917842 9733.7956
95.32 1.1349 108.178668 9085.9024
95.00 1.1621 110.3995 9025
90.65 1.2331 111.780515 8217.4225
88.41 1.2472 110.264952 7816.3281
87.02 1.2672 110.271744 7572.4804
86.05 1.2901 111.013105 7404.6025
82.78 1.3316 110.229848 6852.5284
81.52 1.3539 110.369928 6645.5104
79.81 1.3592 108.477752 6369.6361
80.40 1.3732 110.40528 6464.16
79.53 1.3812 109.846836 6325.0209
80.25 1.3822 110.92155 6440.0625
79.72 1.3658 108.881576 6355.2784
81.40 1.3610 110.7854 6625.96
80.19 1.3703 109.884357 6430.4361
80.66 1.3492 108.826472 6506.0356
80.26 1.3634 109.426484 6441.6676
80.32 1.3347 107.203104 6451.3024
82.14 1.3309 109.320126 6746.9796
81.54 1.3080 106.65432 6648.7716

Step 2: Find the sum of every column:

$$ \sum{X} = 3221.54 ~,~ \sum{Y} = 44.0047 ~,~ \sum{X \cdot Y} = 3906.417053 ~,~ \sum{X^2} = 290362.335 $$

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

$$ \begin{aligned} a &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 44.0047 \cdot 290362.335 - 3221.54 \cdot 3906.417053}{ 36 \cdot 290362.335 - 3221.54^2} \approx 2.578 \\ \\b &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 36 \cdot 3906.417053 - 3221.54 \cdot 44.0047 }{ 36 \cdot 290362.335 - \left( 3221.54 \right)^2} \approx -0.01515\end{aligned}$$

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

$$ \begin{aligned} y~&=~a ~+~ b \cdot x \\y~&=~2.578 ~-~ 0.01515 \cdot x\end{aligned}$$

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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 , 1.1174,1.1311,1.1339,1.1099,1.1092,1.0859,1.0877,1.0736,1.1235,1.1221,1.1139,1.0995,1.1213,1.1149,1.0779,1.0837,1.1349,1.1621,1.2331,1.2472,1.2672,1.2901,1.3316,1.3539,1.3592,1.3732,1.3812,1.3822,1.3658,1.3610,1.3703,1.3492,1.3634,1.3347,1.3309,1.3080 , 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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