Linear regression calculator
This linear regression calculator uses the least squares method to find the line of best fit for a set of paired data. The line of best fit is described by the equation f(x) = Ax + B, where A is the slope of the line and B is the y-axis intercept.All you need is enter paired data into the text box, each pair of x and y each line (row).
Also calculate coefficient of correlation Pearson product-moment correlation coefficient (PPMCC or PCC or R). The Pearson correlation coefficient is used to measure the strength of a linear association between two variables, where the value R = 1 means a perfect positive correlation and the value R = -1 means a perfect negataive correlation.
Calculation:
Statistical file:{[2; 12], [5; 20], [7; 25], [11; 26], [15; 40]}
A = 1.93269230769 (slope)
B = 9.13846153846 (y intercept)
R = 0.962650743928 (correlation coefficient)
y = f(x) = Ax + B = 1.9327x+9.1385
Calculation Summary:
| x | y | xy | x2 | x-mx | y-my | (x-mx)2 | (y-my)2 | (x-mx)(y-my) |
|---|---|---|---|---|---|---|---|---|
| 2 | 12 | 24 | 4 | -6 | -12.6 | 36 | 158.76 | 75.6 |
| 5 | 20 | 100 | 25 | -3 | -4.6 | 9 | 21.16 | 13.8 |
| 7 | 25 | 175 | 49 | -1 | 0.4 | 1 | 0.16 | -0.4 |
| 11 | 26 | 286 | 121 | 3 | 1.4 | 9 | 1.96 | 4.2 |
| 15 | 40 | 600 | 225 | 7 | 15.4 | 49 | 237.16 | 107.8 |
| ∑x = 40 | ∑y = 123 | ∑xy = 1185 | ∑x2 = 424 | mx=8 | my=24.6 | SSX = ∑(y-my))2 = 104 | SSY = ∑(y-my))2 = 419.2 | SP = ∑(x-mx)(y-my) = 201 |
X-data
Average (mean): μ=8
Absolute deviation: 20
Mean deviation: 4
Minimum: 2
Maximum: 15
Variance: 20.8
Standard deviation σ=4.5607017004
Corrected sample standard deviation s=5.09901951359
Coefficient of variation cV=0.637377439199
Signal-to-noise ratio SNR=1.56892908111
Median: 7
Quartile Q1: 3.5
Quartile Q2: 7
Quartile Q3: 13
1st decile: 2 (Too few data to calculate deciles)
2nd decile: 3.5
3rd decile: 5
4th decile: 6
5th decile: 7
6th decile: 9
7th decile: 11
8th decile: 13
9th decile: 15
Interquartile range IQR: 9.5
Quartile Deviation QD: 4.75
Coefficient of Quartile Deviation CQD: 0.575757575758
Lower fence: -10.75
Upper fence: 27.25
Set of outliers: {} - empty set - no outliers found
Interdecile range IDR: 13
Mode: {2, 5, 7, 11, 15} - multimodal
Geometric mean: 6.49406149528
Harmonic mean: 4.99783643444
Sum: 40
Sum of squares: 104
Sum of absolute values: 40
Average absolute deviation: 4
Range: 13
Frequency table :
| element | frequency | cumulative frequency | relative frequency | cumulative relative frequency |
|---|---|---|---|---|
| 2 | 1 | 1 | 0.2 | 0.2 |
| 5 | 1 | 2 | 0.2 | 0.4 |
| 7 | 1 | 3 | 0.2 | 0.6 |
| 11 | 1 | 4 | 0.2 | 0.8 |
| 15 | 1 | 5 | 0.2 | 1 |
Count items: 5
Calculation of normal distribution
Statistical file(X-data):
{2, 5, 7, 11, 15}
Y-data
Average (mean): μ=8
Absolute deviation: 83
Mean deviation: 16.6
Minimum: 12
Maximum: 40
Variance: 359.4
Standard deviation σ=18.9578479791
Corrected sample standard deviation s=21.1955183942
Coefficient of variation cV=2.64943979928
Signal-to-noise ratio SNR=0.377438279697
Median: 25
Quartile Q1: 16
Quartile Q2: 25
Quartile Q3: 33
1st decile: 12 (Too few data to calculate deciles)
2nd decile: 16
3rd decile: 20
4th decile: 22.5
5th decile: 25
6th decile: 25.5
7th decile: 26
8th decile: 33
9th decile: 40
Interquartile range IQR: 17
Quartile Deviation QD: 8.5
Coefficient of Quartile Deviation CQD: 0.34693877551
Lower fence: -9.5
Upper fence: 58.5
Set of outliers: {} - empty set - no outliers found
Interdecile range IDR: 28
Mode: {2, 5, 7, 11, 15} - multimodal
Geometric mean: 22.8579310282
Harmonic mean: 21.115322144
Sum: 40
Sum of squares: 1797
Sum of absolute values: 123
Average absolute deviation: 16.6
Range: 28
Frequency table :
| element | frequency | cumulative frequency | relative frequency | cumulative relative frequency |
|---|---|---|---|---|
| 2 | 1 | 1 | 0.2 | 0.2 |
| 5 | 1 | 2 | 0.2 | 0.4 |
| 7 | 1 | 3 | 0.2 | 0.6 |
| 11 | 1 | 4 | 0.2 | 0.8 |
| 15 | 1 | 5 | 0.2 | 1 |
Count items: 5
Calculation of normal distribution
Statistical file(Y-data):
{12, 20, 25, 26, 40}