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:

$$\begin{array}{c|ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc}X&3&11&4&29&21&39&14&30&21&11&2&4&16&30&44&20&15&36&30&60&30&4&13&23&1&36&24&11&21&30&2&17&21&30&21&23&20&23&23&59&23&28&30&30&30&30&38&7&16&30&43&22&30&59&30&37&4&29&30&30&30&28&5&30&24&30&24&30&20&30&6&37&54&24&24&24&24&26&29&29&30&30&11&30&11&24&28&28&30&30&50&24&28&30&30&30&30&22&38&54&11&36&24&15&30&30&24&59&52&36&21&30&57&52&6&48&30&22&23&49&11&11&37&62&37&45&46&62&14&17&30&30&49&57&39&49&51\\Y&5255&5000&4900&4544&4522&4195&4109&4100&3900&3700&3309&3309&3309&3305&3300&3300&3220&3209&3209&3200&3200&3150&3150&3109&3101&3100&3100&3099&3000&2999&2900&2900&2900&2900&2809&2809&2800&2800&2722&2700&2700&2700&2700&2700&2700&2700&2671&2650&2650&2650&2622&2609&2609&2601&2601&2600&2600&2600&2600&2600&2600&2599&2550&2550&2531&2528&2520&2520&2510&2509&2503&2500&2500&2500&2500&2500&2500&2500&2500&2500&2500&2500&2499&2488&2450&2450&2450&2450&2450&2450&2422&2401&2400&2400&2400&2400&2388&2381&2320&2319&2309&2301&2301&2300&2300&2300&2299&2290&2260&2238&2222&2214&2210&2201&2201&2200&2188&2180&2160&2150&2131&2129&2124&2119&2100&2100&2100&2100&2100&2100&2100&2100&2098&2085&2050&2010&2010\end{array}$$

The equation of the regression line is:

$$y~=~3127 ~-~ 15.52 \cdot x$$

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.

$X$	$Y$	$X\cdot Y$	$X \cdot X$
3	5255	15765	9
11	5000	55000	121
4	4900	19600	16
29	4544	131776	841
21	4522	94962	441
39	4195	163605	1521
14	4109	57526	196
30	4100	123000	900
21	3900	81900	441
11	3700	40700	121
2	3309	6618	4
4	3309	13236	16
16	3309	52944	256
30	3305	99150	900
44	3300	145200	1936
20	3300	66000	400
15	3220	48300	225
36	3209	115524	1296
30	3209	96270	900
60	3200	192000	3600
30	3200	96000	900
4	3150	12600	16
13	3150	40950	169
23	3109	71507	529
1	3101	3101	1
36	3100	111600	1296
24	3100	74400	576
11	3099	34089	121
21	3000	63000	441
30	2999	89970	900
2	2900	5800	4
17	2900	49300	289
21	2900	60900	441
30	2900	87000	900
21	2809	58989	441
23	2809	64607	529
20	2800	56000	400
23	2800	64400	529
23	2722	62606	529
59	2700	159300	3481
23	2700	62100	529
28	2700	75600	784
30	2700	81000	900
30	2700	81000	900
30	2700	81000	900
30	2700	81000	900
38	2671	101498	1444
7	2650	18550	49
16	2650	42400	256
30	2650	79500	900

Step 2: Find the sum of every column:

$$ \sum{X} = 3866 ~,~ \sum{Y} = 368324 ~,~ \sum{X \cdot Y} = 9973627 ~,~ \sum{X^2} = 136158 $$

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

$$ \begin{aligned} a &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 368324 \cdot 136158 - 3866 \cdot 9973627}{ 137 \cdot 136158 - 3866^2} \approx 3127 \\ \\b &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 137 \cdot 9973627 - 3866 \cdot 368324 }{ 137 \cdot 136158 - \left( 3866 \right)^2} \approx -15.52\end{aligned}$$

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

$$ \begin{aligned} y~&=~a ~+~ b \cdot x \\y~&=~3127 ~-~ 15.52 \cdot x\end{aligned}$$

Report an Error !

Script name : correlation-and-regression-calculator

Form values: 3 11 4 29 21 39 14 30 21 11 2 4 16 30 44 20 15 36 30 60 30 4 13 23 1 36 24 11 21 30 2 17 21 30 21 23 20 23 23 59 23 28 30 30 30 30 38 7 16 30 43 22 30 59 30 37 4 29 30 30 30 28 5 30 24 30 24 30 20 30 6 37 54 24 24 24 24 26 29 29 30 30 11 30 11 24 28 28 30 30 50 24 28 30 30 30 30 22 38 54 11 36 24 15 30 30 24 59 52 36 21 30 57 52 6 48 30 22 23 49 11 11 37 62 37 45 46 62 14 17 30 30 49 57 39 49 51 , 5255 5000 4900 4544 4522 4195 4109 4100 3900 3700 3309 3309 3309 3305 3300 3300 3220 3209 3209 3200 3200 3150 3150 3109 3101 3100 3100 3099 3000 2999 2900 2900 2900 2900 2809 2809 2800 2800 2722 2700 2700 2700 2700 2700 2700 2700 2671 2650 2650 2650 2622 2609 2609 2601 2601 2600 2600 2600 2600 2600 2600 2599 2550 2550 2531 2528 2520 2520 2510 2509 2503 2500 2500 2500 2500 2500 2500 2500 2500 2500 2500 2500 2499 2488 2450 2450 2450 2450 2450 2450 2422 2401 2400 2400 2400 2400 2388 2381 2320 2319 2309 2301 2301 2300 2300 2300 2299 2290 2260 2238 2222 2214 2210 2201 2201 2200 2188 2180 2160 2150 2131 2129 2124 2119 2100 2100 2100 2100 2100 2100 2100 2100 2098 2085 2050 2010 2010 , reg , g , , , , Regression line X = [ 3 11 4 29 21 39 14 30 21 11 2 4 16 30 44 20 15 36 30 60 30 4 13 23 1 36 24 11 21 30 2 17 21 30 21 23 20 23 23 59 23 28 30 30 30 30 38 7 16 30 43 22 30 59 30 37 4 29 30 30 30 28 5 30 24 30 24 30 20 30 6 37 54 24 24 24 24 26 29 29 30 30 11 30 11 24 28 28 30 30 50 24 28 30 30 30 30 22 38 54 11 36 24 15 30 30 24 59 52 36 21 30 57 52 6 48 30 22 23 49 11 11 37 62 37 45 46 62 14 17 30 30 49 57 39 49 51 ] , Y = [ 5255 5000 4900 4544 4522 4195 4109 4100 3900 3700 3309 3309 3309 3305 3300 3300 3220 3209 3209 3200 3200 3150 3150 3109 3101 3100 3100 3099 3000 2999 2900 2900 2900 2900 2809 2809 2800 2800 2722 2700 2700 2700 2700 2700 2700 2700 2671 2650 2650 2650 2622 2609 2609 2601 2601 2600 2600 2600 2600 2600 2600 2599 2550 2550 2531 2528 2520 2520 2510 2509 2503 2500 2500 2500 2500 2500 2500 2500 2500 2500 2500 2500 2499 2488 2450 2450 2450 2450 2450 2450 2422 2401 2400 2400 2400 2400 2388 2381 2320 2319 2309 2301 2301 2300 2300 2300 2299 2290 2260 2238 2222 2214 2210 2201 2201 2200 2188 2180 2160 2150 2131 2129 2124 2119 2100 2100 2100 2100 2100 2100 2100 2100 2098 2085 2050 2010 2010 ]

Comment (optional)

Share Result

You can copy and paste the link wherever you need it.

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

Hide steps

working...