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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:

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

The equation of the regression line is:

$$y~=~2352 ~-~ 0.6273 \cdot x$$

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

Step 2: Find the sum of every column:

$$ \sum{X} = 535 ~,~ \sum{Y} = 77295 ~,~ \sum{X \cdot Y} = 1251090 ~,~ \sum{X^2} = 11903 $$

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

$$ \begin{aligned} a &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 77295 \cdot 11903 - 535 \cdot 1251090}{ 33 \cdot 11903 - 535^2} \approx 2352 \\ \\b &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 33 \cdot 1251090 - 535 \cdot 77295 }{ 33 \cdot 11903 - \left( 535 \right)^2} \approx -0.6273\end{aligned}$$

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

$$ \begin{aligned} y~&=~a ~+~ b \cdot x \\y~&=~2352 ~-~ 0.6273 \cdot x\end{aligned}$$

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Script name : correlation-and-regression-calculator

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