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:

$$\begin{array}{c|cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc}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end{array}$$

The equation of the regression line is:

$$y~=~3693 ~-~ 4.258 \cdot x$$

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.

$X$	$Y$	$X\cdot Y$	$X \cdot X$
18	5290	95220	324
24	5109	122616	576
30	4611	138330	900
36	4400	158400	1296
30	4400	132000	900
28	4400	123200	784
30	4320	129600	900
30	4310	129300	900
21	4309	90489	441
44	4300	189200	1936
57	4300	245100	3249
30	4209	126270	900
44	4200	184800	1936
44	4200	184800	1936
11	4160	45760	121
11	4120	45320	121
8	4110	32880	64
49	4100	200900	2401
37	4100	151700	1369
7	4100	28700	49
8	4100	32800	64
37	4009	148333	1369
30	4009	120270	900
14	3920	54880	196
26	3900	101400	676
57	3866	220362	3249
36	3810	137160	1296
18	3809	68562	324
24	3809	91416	576
29	3802	110258	841
44	3800	167200	1936
34	3800	129200	1156
36	3800	136800	1296
36	3800	136800	1296
37	3800	140600	1369
37	3800	140600	1369
7	3800	26600	49
27	3800	102600	729
29	3800	110200	841
31	3800	117800	961
31	3800	117800	961
30	3730	111900	900
23	3709	85307	529
23	3702	85146	529
34	3700	125800	1156
36	3700	133200	1296
45	3700	166500	2025
37	3700	136900	1369
44	3700	162800	1936
30	3700	111000	900

Step 2: Find the sum of every column:

$$ \sum{X} = 5974 ~,~ \sum{Y} = 617090 ~,~ \sum{X \cdot Y} = 21015151 ~,~ \sum{X^2} = 245412 $$

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

$$ \begin{aligned} a &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 617090 \cdot 245412 - 5974 \cdot 21015151}{ 174 \cdot 245412 - 5974^2} \approx 3693 \\ \\b &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 174 \cdot 21015151 - 5974 \cdot 617090 }{ 174 \cdot 245412 - \left( 5974 \right)^2} \approx -4.258\end{aligned}$$

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

$$ \begin{aligned} y~&=~a ~+~ b \cdot x \\y~&=~3693 ~-~ 4.258 \cdot x\end{aligned}$$

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Script name : correlation-and-regression-calculator

Form values: 18 24 30 36 30 28 30 30 21 44 57 30 44 44 11 11 8 49 37 7 8 37 30 14 26 57 36 18 24 29 44 34 36 36 37 37 7 27 29 31 31 30 23 23 34 36 45 37 44 30 30 30 30 24 49 30 15 23 22 1 44 44 44 44 11 24 3 47 9 29 12 30 44 30 24 46 30 44 60 44 49 49 49 41 41 43 49 45 45 36 46 14 19 30 24 24 15 24 49 30 44 24 10 57 43 44 45 10 28 24 57 60 39 57 47 57 45 44 39 50 24 57 44 49 9 62 51 62 49 60 60 24 9 27 28 50 51 52 51 54 3 51 24 55 2 62 52 14 50 53 30 44 39 45 20 11 44 62 52 14 11 9 24 44 57 44 24 24 30 30 28 28 15 24 , 5290 5109 4611 4400 4400 4400 4320 4310 4309 4300 4300 4209 4200 4200 4160 4120 4110 4100 4100 4100 4100 4009 4009 3920 3900 3866 3810 3809 3809 3802 3800 3800 3800 3800 3800 3800 3800 3800 3800 3800 3800 3730 3709 3702 3700 3700 3700 3700 3700 3700 3700 3700 3700 3683 3660 3621 3620 3620 3605 3601 3600 3600 3600 3600 3600 3600 3581 3577 3530 3529 3524 3520 3510 3510 3505 3502 3502 3500 3500 3500 3500 3500 3500 3500 3500 3500 3500 3500 3500 3500 3500 3500 3500 3500 3500 3500 3429 3422 3420 3419 3411 3410 3409 3401 3400 3400 3400 3400 3400 3400 3390 3390 3388 3377 3377 3376 3360 3350 3350 3350 3320 3319 3312 3310 3309 3300 3300 3300 3300 3300 3300 3300 3300 3300 3255 3250 3250 3250 3250 3250 3250 3243 3230 3220 3220 3210 3210 3209 3202 3202 3202 3200 3200 3200 3200 3120 3110 3100 3100 3100 3100 3100 3100 3010 3000 3000 3000 2929 2922 2920 2900 2900 2851 2803 , reg , g , , , , Regression line X = [ 18 24 30 36 30 28 30 30 21 44 57 30 44 44 11 11 8 49 37 7 8 37 30 14 26 57 36 18 24 29 44 34 36 36 37 37 7 27 29 31 31 30 23 23 34 36 45 37 44 30 30 30 30 24 49 30 15 23 22 1 44 44 44 44 11 24 3 47 9 29 12 30 44 30 24 46 30 44 60 44 49 49 49 41 41 43 49 45 45 36 46 14 19 30 24 24 15 24 49 30 44 24 10 57 43 44 45 10 28 24 57 60 39 57 47 57 45 44 39 50 24 57 44 49 9 62 51 62 49 60 60 24 9 27 28 50 51 52 51 54 3 51 24 55 2 62 52 14 50 53 30 44 39 45 20 11 44 62 52 14 11 9 24 44 57 44 24 24 30 30 28 28 15 24 ] , Y = [ 5290 5109 4611 4400 4400 4400 4320 4310 4309 4300 4300 4209 4200 4200 4160 4120 4110 4100 4100 4100 4100 4009 4009 3920 3900 3866 3810 3809 3809 3802 3800 3800 3800 3800 3800 3800 3800 3800 3800 3800 3800 3730 3709 3702 3700 3700 3700 3700 3700 3700 3700 3700 3700 3683 3660 3621 3620 3620 3605 3601 3600 3600 3600 3600 3600 3600 3581 3577 3530 3529 3524 3520 3510 3510 3505 3502 3502 3500 3500 3500 3500 3500 3500 3500 3500 3500 3500 3500 3500 3500 3500 3500 3500 3500 3500 3500 3429 3422 3420 3419 3411 3410 3409 3401 3400 3400 3400 3400 3400 3400 3390 3390 3388 3377 3377 3376 3360 3350 3350 3350 3320 3319 3312 3310 3309 3300 3300 3300 3300 3300 3300 3300 3300 3300 3255 3250 3250 3250 3250 3250 3250 3243 3230 3220 3220 3210 3210 3209 3202 3202 3202 3200 3200 3200 3200 3120 3110 3100 3100 3100 3100 3100 3100 3010 3000 3000 3000 2929 2922 2920 2900 2900 2851 2803 ]

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Correlation and Regression Calculator

Input X and Y values separated by comma or blank space
help ↓↓ examples ↓↓

Enter X Values:

Enter Y Values:

Use data grit to input x and y values

Choose what to compute:

Find the equation of the regression line

Find the correlation coefficient

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