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], [0; 0], [5; 20], [0; 0], [7; 25], [0; 0], [11; 26], [0; 0], [15; 40]}
A = 2.5925090252708 (slope)
B = 2.14440433213 (y intercept)
R = 0.96857802117607 (correlation coefficient)
y = f(x) = Ax + B = 2.5925x+2.1444
Calculation Summary:
| x | y | xy | x2 | x-mx | y-my | (x-mx)2 | (y-my)2 | (x-mx)(y-my) |
|---|---|---|---|---|---|---|---|---|
| 2 | 12 | 24 | 4 | -2.4444444444444 | -1.6666666666667 | 5.9753086419753 | 2.7777777777778 | 4.0740740740741 |
| 0 | 0 | 0 | 0 | -4.4444444444444 | -13.666666666667 | 19.753086419753 | 186.77777777778 | 60.740740740741 |
| 5 | 20 | 100 | 25 | 0.55555555555556 | 6.3333333333333 | 0.30864197530864 | 40.111111111111 | 3.5185185185185 |
| 0 | 0 | 0 | 0 | -4.4444444444444 | -13.666666666667 | 19.753086419753 | 186.77777777778 | 60.740740740741 |
| 7 | 25 | 175 | 49 | 2.5555555555556 | 11.333333333333 | 6.5308641975309 | 128.44444444444 | 28.962962962963 |
| 0 | 0 | 0 | 0 | -4.4444444444444 | -13.666666666667 | 19.753086419753 | 186.77777777778 | 60.740740740741 |
| 11 | 26 | 286 | 121 | 6.5555555555556 | 12.333333333333 | 42.975308641975 | 152.11111111111 | 80.851851851852 |
| 0 | 0 | 0 | 0 | -4.4444444444444 | -13.666666666667 | 19.753086419753 | 186.77777777778 | 60.740740740741 |
| 15 | 40 | 600 | 225 | 10.555555555556 | 26.333333333333 | 111.41975308642 | 693.44444444444 | 277.96296296296 |
| ∑x = 40 | ∑y = 123 | ∑xy = 1185 | ∑x2 = 424 | mx=4.4444444444444 | my=13.666666666667 | SSX = ∑(y-my))2 = 246.22222222222 | SSY = ∑(y-my))2 = 1764 | SP = ∑(x-mx)(y-my) = 638.33333333333 |
X-data
Average (mean): μ=4.4444444444444
Absolute deviation: 40.444444444444
Mean deviation: 4.4938271604938
Minimum: 0
Maximum: 15
Variance: 27.358024691358
Standard deviation σ=5.2304899093066
Corrected sample standard deviation s=5.5477723256977
Coefficient of variation cV=1.248248773282
Signal-to-noise ratio SNR=0.80112235750148
Median: 2
Quartile Q1: 0
Quartile Q2: 2
Quartile Q3: 9
1st decile: 0 (Too few data to calculate deciles)
2nd decile: 0
3rd decile: 0
4th decile: 0
5th decile: 2
6th decile: 5
7th decile: 7
8th decile: 11
9th decile: 15
Interquartile range IQR: 9
Quartile Deviation QD: 4.5
Coefficient of Quartile Deviation CQD: 1
Lower fence: -13.5
Upper fence: 22.5
Set of outliers: {} - empty set - no outliers found
Interdecile range IDR: 15
Mode: 0 - unimodal
Geometric mean: 0
Harmonic mean: 0
Sum: 40
Sum of squares: 246.22222222222
Sum of absolute values: 40
Average absolute deviation: 4.4938271604938
Range: 15
Frequency table :
| element | frequency | cumulative frequency | relative frequency | cumulative relative frequency |
|---|---|---|---|---|
| 0 | 4 | 4 | 0.44444444444444 | 0.44444444444444 |
| 2 | 1 | 5 | 0.11111111111111 | 0.55555555555556 |
| 5 | 1 | 6 | 0.11111111111111 | 0.66666666666667 |
| 7 | 1 | 7 | 0.11111111111111 | 0.77777777777778 |
| 11 | 1 | 8 | 0.11111111111111 | 0.88888888888889 |
| 15 | 1 | 9 | 0.11111111111111 | 1 |
Count items: 9
Calculation of normal distribution
Statistical file(X-data):
{0, 0, 0, 0, 2, 5, 7, 11, 15}
Y-data
Average (mean): μ=13.666666666667
Absolute deviation: 112.66666666667
Mean deviation: 12.518518518519
Minimum: 0
Maximum: 40
Variance: 196
Standard deviation σ=14
Corrected sample standard deviation s=14.849242404917
Coefficient of variation cV=1.0865299320671
Signal-to-noise ratio SNR=0.92036120725868
Median: 12
Quartile Q1: 0
Quartile Q2: 12
Quartile Q3: 25.5
1st decile: 0 (Too few data to calculate deciles)
2nd decile: 0
3rd decile: 0
4th decile: 0
5th decile: 12
6th decile: 20
7th decile: 25
8th decile: 26
9th decile: 40
Interquartile range IQR: 25.5
Quartile Deviation QD: 12.75
Coefficient of Quartile Deviation CQD: 1
Lower fence: -38.25
Upper fence: 63.75
Set of outliers: {} - empty set - no outliers found
Interdecile range IDR: 40
Mode: 0 - unimodal
Geometric mean: 0
Harmonic mean: 0
Sum: 123
Sum of squares: 1764
Sum of absolute values: 123
Average absolute deviation: 12.518518518519
Range: 40
Frequency table :
| element | frequency | cumulative frequency | relative frequency | cumulative relative frequency |
|---|---|---|---|---|
| 0 | 4 | 4 | 0.44444444444444 | 0.44444444444444 |
| 12 | 1 | 5 | 0.11111111111111 | 0.55555555555556 |
| 20 | 1 | 6 | 0.11111111111111 | 0.66666666666667 |
| 25 | 1 | 7 | 0.11111111111111 | 0.77777777777778 |
| 26 | 1 | 8 | 0.11111111111111 | 0.88888888888889 |
| 40 | 1 | 9 | 0.11111111111111 | 1 |
Count items: 9
Calculation of normal distribution
Statistical file(Y-data):
{0, 0, 0, 0, 12, 20, 25, 26, 40}
Practice problems from statistics:
- Employees 70614
The company has 18 employees aged 26-52. The age groups of the employees are: 3 employees aged 52 years, 2 aged 32 years, 1 ... 26 years old, 5 ... 36 years old, 4 ... 45 years old, and 3 ... 50 years old. Determine the median. - The median 2
Here is a list of numbers: 9.9, 5.9, 3.6, 6.2, 8.9, 0.7, 4.4, 6.7, 9.9, 0.7 State the median. Give your answer as a decimal. - Median and modus
Radka made 50 throws with a dice. The table saw fit individual dice's wall frequency: Wall Number: 1 2 3 4 5 6 frequency: 8 7 5 11 6 13 Calculate the modus and median of the wall numbers that Radka fell. - Third tests Third periodical tests are 98, 97, 86, 94, 90, 97, 91, and 94. Find the median of her grades and interpret the result.
- Increase the mean
To which number should the number 4 be changed between the numbers 4,5,7, 1,0,9,7,8, -3,5 to increase these numbers' arithmetic mean by 1.25? - A Gallup
A Gallup poll investigated whether adults in Mumbai preferred staying at home or going out as their favorite way of spending time in the evening. Out of the 500 adults, the majority of adults (70%) indicated that staying at home was their favorite evening - The size 2
The size of pants sold during one business day in a department store is 32, 38, 34, 42, 36, 34, 40, 44, 32, and 34. Find the average size of the pants sold. - Find mean
Find mean of two numbers: -4 and 5 (first is negative four). - Harmonic HM example
Find the harmonic mean of 4 and 8.
- Below 5
Below is a collection of test scores from a class of 20 students. Make 2 histograms of the data. Choose your own horizontal scales as long as you have more than 4 cells in each histogram. 65 70 68 87 98 91 77 85 70 72 86 86 94 95 67 88 77 99 74 71 - 75th percentile (quartille Q3)
Find 75th percentile for 30,42,42,46,46,46,50,50,54
more math problems »