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:

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

The equation of the regression line is:

$$y~=~3815 ~-~ 6.559 \cdot x$$

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.

$X$	$Y$	$X\cdot Y$	$X \cdot X$
62	3300	204600	3844
51	3243	165393	2601
44	3800	167200	1936
44	3510	154440	1936
44	3600	158400	1936
57	3401	193857	3249
44	3312	145728	1936
57	3000	171000	3249
62	3210	199020	3844
43	3400	146200	1849
50	3202	160100	2500
57	3376	192432	3249
44	3500	154000	1936
45	3360	151200	2025
49	4100	200900	2401
60	3500	210000	3600
44	3000	132000	1936
44	3010	132440	1936
62	3100	192200	3844
44	4200	184800	1936
44	4200	184800	1936
44	3600	158400	1936
51	3300	168300	2601
34	3700	125800	1156
44	3600	158400	1936
34	3800	129200	1156
44	3411	150084	1936
62	3300	204600	3844
36	4400	158400	1296
44	3500	154000	1936
36	3800	136800	1296
36	3700	133200	1296
44	3600	158400	1936
44	3200	140800	1936
37	4100	151700	1369
44	3110	136840	1936
49	3500	171500	2401
44	3350	147400	1936
44	3400	149600	1936
39	3350	130650	1521
39	3200	124800	1521
39	3388	132132	1521
49	3500	171500	2401
49	3310	162190	2401
49	3500	171500	2401
41	3500	143500	1681
41	3500	143500	1681
43	3500	150500	1849
49	3500	171500	2401
49	3300	161700	2401

Step 2: Find the sum of every column:

$$ \sum{X} = 5996 ~,~ \sum{Y} = 628280 ~,~ \sum{X \cdot Y} = 21261331 ~,~ \sum{X^2} = 245896 $$

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

$$ \begin{aligned} a &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 628280 \cdot 245896 - 5996 \cdot 21261331}{ 175 \cdot 245896 - 5996^2} \approx 3815 \\ \\b &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 175 \cdot 21261331 - 5996 \cdot 628280 }{ 175 \cdot 245896 - \left( 5996 \right)^2} \approx -6.559\end{aligned}$$

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

$$ \begin{aligned} y~&=~a ~+~ b \cdot x \\y~&=~3815 ~-~ 6.559 \cdot x\end{aligned}$$

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Script name : correlation-and-regression-calculator

Form values: 62 51 44 44 44 57 44 57 62 43 50 57 44 45 49 60 44 44 62 44 44 44 51 34 44 34 44 62 36 44 36 36 44 44 37 44 49 44 44 39 39 39 49 49 49 41 41 43 49 49 49 44 49 45 45 45 45 46 36 45 46 57 57 36 57 47 37 47 36 57 60 57 37 60 60 50 50 51 52 51 37 52 37 52 54 53 55 44 3 15 24 14 24 24 12 23 30 15 30 24 3 11 11 15 24 30 1 11 24 24 9 30 14 24 2 24 11 20 7 7 8 8 14 19 9 9 14 11 10 10 9 24 30 30 30 18 18 30 22 30 30 30 30 30 22 30 28 23 30 23 24 21 30 24 24 24 28 24 24 24 30 26 27 29 28 27 28 29 28 29 30 30 30 31 31 , 3300 3243 3800 3510 3600 3401 3312 3000 3210 3400 3202 3376 3500 3360 4100 3500 3000 3010 3100 4200 4200 3600 3300 3700 3600 3800 3411 3300 4400 3500 3800 3700 3600 3200 4100 3110 3500 3350 3400 3350 3200 3388 3500 3310 3500 3500 3500 3500 3500 3300 3420 4300 3660 3700 3200 3500 3500 3502 3500 3400 3500 3319 3866 3810 3377 3377 4009 3577 3800 3390 3390 4300 3700 3300 3300 3350 3250 3250 3250 3250 3800 3100 3800 3210 3250 3202 3220 3700 3581 3429 3000 3100 2803 2929 3524 3709 2920 3620 2922 3320 3250 3120 4160 2851 3230 3419 3601 3100 3410 3505 3100 4400 3500 3100 3220 3300 4120 3200 3800 4100 4110 4100 3920 3500 3300 3309 3209 3600 3400 3409 3530 3422 3202 4320 4310 3809 5290 3502 11190 3510 4611 3700 3500 3621 3605 3730 3400 3702 3520 3620 5109 4309 4209 3400 3683 3500 4400 3809 3600 3500 4009 3900 3800 3800 3255 3300 2900 3529 2900 3802 3700 3700 3700 3800 3800 , reg , g , , , , Regression line X = [ 62 51 44 44 44 57 44 57 62 43 50 57 44 45 49 60 44 44 62 44 44 44 51 34 44 34 44 62 36 44 36 36 44 44 37 44 49 44 44 39 39 39 49 49 49 41 41 43 49 49 49 44 49 45 45 45 45 46 36 45 46 57 57 36 57 47 37 47 36 57 60 57 37 60 60 50 50 51 52 51 37 52 37 52 54 53 55 44 3 15 24 14 24 24 12 23 30 15 30 24 3 11 11 15 24 30 1 11 24 24 9 30 14 24 2 24 11 20 7 7 8 8 14 19 9 9 14 11 10 10 9 24 30 30 30 18 18 30 22 30 30 30 30 30 22 30 28 23 30 23 24 21 30 24 24 24 28 24 24 24 30 26 27 29 28 27 28 29 28 29 30 30 30 31 31 ] , Y = [ 3300 3243 3800 3510 3600 3401 3312 3000 3210 3400 3202 3376 3500 3360 4100 3500 3000 3010 3100 4200 4200 3600 3300 3700 3600 3800 3411 3300 4400 3500 3800 3700 3600 3200 4100 3110 3500 3350 3400 3350 3200 3388 3500 3310 3500 3500 3500 3500 3500 3300 3420 4300 3660 3700 3200 3500 3500 3502 3500 3400 3500 3319 3866 3810 3377 3377 4009 3577 3800 3390 3390 4300 3700 3300 3300 3350 3250 3250 3250 3250 3800 3100 3800 3210 3250 3202 3220 3700 3581 3429 3000 3100 2803 2929 3524 3709 2920 3620 2922 3320 3250 3120 4160 2851 3230 3419 3601 3100 3410 3505 3100 4400 3500 3100 3220 3300 4120 3200 3800 4100 4110 4100 3920 3500 3300 3309 3209 3600 3400 3409 3530 3422 3202 4320 4310 3809 5290 3502 11190 3510 4611 3700 3500 3621 3605 3730 3400 3702 3520 3620 5109 4309 4209 3400 3683 3500 4400 3809 3600 3500 4009 3900 3800 3800 3255 3300 2900 3529 2900 3802 3700 3700 3700 3800 3800 ]

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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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