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Correlation and regression calculator

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

solution

You entered the following data:

$$\begin{array}{c|cccccccccccccccccccccccccccccccccccc}X&23&25&29&26&29&2&29&23&5&18&5&1&19&19&26&1&3&17&12&19&26&26&18&4&27&4&25&1&17&3&1&1&17&29&22&12\\Y&2560&2200&2100&2400&2400&4050&2100&2300&2600&2700&2701&2110&2301&2501&4300&2400&2107&2350&2319&2212&2089&2500&2400&2910&2250&2047&2100&3433&2200&2400&2119&2019&2800&2200&2900&2000\end{array}$$

The equation of the regression line is:

$$y~=~2563 ~-~ 5.638 \cdot x$$

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$ 
23 2560 58880 529
25 2200 55000 625
29 2100 60900 841
26 2400 62400 676
29 2400 69600 841
2 4050 8100 4
29 2100 60900 841
23 2300 52900 529
5 2600 13000 25
18 2700 48600 324
5 2701 13505 25
1 2110 2110 1
19 2301 43719 361
19 2501 47519 361
26 4300 111800 676
1 2400 2400 1
3 2107 6321 9
17 2350 39950 289
12 2319 27828 144
19 2212 42028 361
26 2089 54314 676
26 2500 65000 676
18 2400 43200 324
4 2910 11640 16
27 2250 60750 729
4 2047 8188 16
25 2100 52500 625
1 3433 3433 1
17 2200 37400 289
3 2400 7200 9
1 2119 2119 1
1 2019 2019 1
17 2800 47600 289
29 2200 63800 841
22 2900 63800 484
12 2000 24000 144

Step 2: Find the sum of every column:

$$ \sum{X} = 564 ~,~ \sum{Y} = 89078 ~,~ \sum{X \cdot Y} = 1374423 ~,~ \sum{X^2} = 12584 $$

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

$$ \begin{aligned} a &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 89078 \cdot 12584 - 564 \cdot 1374423}{ 36 \cdot 12584 - 564^2} \approx 2563 \\ \\b &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 36 \cdot 1374423 - 564 \cdot 89078 }{ 36 \cdot 12584 - \left( 564 \right)^2} \approx -5.638\end{aligned}$$

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

$$ \begin{aligned} y~&=~a ~+~ b \cdot x \\y~&=~2563 ~-~ 5.638 \cdot x\end{aligned}$$

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Script name : correlation-and-regression-calculator

Form values: 23 25 29 26 29 2 29 23 5 18 5 1 19 19 26 1 3 17 12 19 26 26 18 4 27 4 25 1 17 3 1 1 17 29 22 12 , 2560 2200 2100 2400 2400 4050 2100 2300 2600 2700 2701 2110 2301 2501 4300 2400 2107 2350 2319 2212 2089 2500 2400 2910 2250 2047 2100 3433 2200 2400 2119 2019 2800 2200 2900 2000 , reg , g , , , , Regression line X = [ 23 25 29 26 29 2 29 23 5 18 5 1 19 19 26 1 3 17 12 19 26 26 18 4 27 4 25 1 17 3 1 1 17 29 22 12 ] , Y = [ 2560 2200 2100 2400 2400 4050 2100 2300 2600 2700 2701 2110 2301 2501 4300 2400 2107 2350 2319 2212 2089 2500 2400 2910 2250 2047 2100 3433 2200 2400 2119 2019 2800 2200 2900 2000 ]

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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 correlation 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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