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Correlation and regression calculator

Enter two data sets and this calculator will find the equation of the regression line and corelation coefficient. The calculator will generate a step by step explanation along with the graphic representation of the data sets and regression line.

Result:

You entered the following data:

$$\begin{array}{c|cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc}X&1.1174&1.1311&1.1339&1.1099&1.1092&1.0859&1.0877&1.0736&1.1235&1.1221&1.1139&1.0995&1.1213&1.1149&1.0779&1.0837&1.1349&1.1621&1.2331&1.2472&1.2672&1.2901&1.3316&1.3539&1.3592&1.3732&1.3812&1.3822&1.3658&1.3610&1.3703&1.3492&1.3634&1.3347&1.3309&1.3080&1.3188&1.2982&1.3026&1.2963&1.3359&1.3288&1.3119&1.2827&1.2974&1.2855&1.2399&1.2288&1.2526&1.2788&1.3161&1.3201&1.3224&1.2904&1.3179&1.3555&1.3706&1.3770&1.4343&1.4264&1.4388&1.4348&1.4441&1.3996&1.3648&1.3359&1.3220&1.3660&1.3897&1.3067&1.2894&1.2767&1.2208&1.2565&1.3405&1.3568&1.3685&1.4272&1.4613&1.4911&1.4816&1.4561&1.4268&1.4087&1.4016&1.3650&1.3190&1.3049&1.2784&1.3238&1.3449&1.2732&1.3322&1.4369&1.4975&1.5769&1.5552&1.5557&1.5750&1.5526&1.4748&1.4717&1.4570&1.4683&1.4227&1.3896&1.3622&1.3715&1.3418&1.3511&1.3516&1.3241&1.3074&1.2998&1.3212&1.2881&1.2611&1.2730&1.2811&1.2683\\Y&95.42&95.88&93.05&94.58&98.22&99.65&98.75&100.21&97.02&96.48&95.85&97.44&95.66&96.99&94.71&98.66&95.32&95.00&90.65&88.41&87.02&86.05&82.78&81.52&79.81&80.40&79.53&80.25&79.72&81.40&80.19&80.66&80.26&80.32&82.14&81.54&83.38&83.40&81.81&83.17&82.00&79.23&79.87&80.16&79.99&80.03&81.22&82.71&81.75&83.13&78.85&79.14&78.79&79.42&80.52&78.49&76.31&79.08&74.17&74.04&74.64&74.70&73.11&76.07&76.92&77.86&79.29&81.27&77.46&78.94&83.25&81.66&86.28&86.67&81.99&81.29&80.44&79.65&78.22&74.94&76.47&76.86&78.22&78.45&80.42&79.43&84.78&85.89&88.15&86.46&82.15&86.70&86.34&79.36&77.50&73.42&72.80&72.95&72.72&72.17&73.75&75.28&76.70&76.17&76.46&77.62&80.75&80.66&81.69&82.25&81.30&82.66&83.50&84.43&83.43&82.85&85.11&85.68&85.02&85.09\end{array}$$

The equation of the regression line is:

$$y~=~156.4 ~-~ 55.75 \cdot x$$

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.

 $X$ $Y$ $X\cdot Y$ $X \cdot X$ 1.1174 95.42 106.622308 1.24858276 1.1311 95.88 108.449868 1.27938721 1.1339 93.05 105.509395 1.28572921 1.1099 94.58 104.974342 1.23187801 1.1092 98.22 108.945624 1.23032464 1.0859 99.65 108.209935 1.17917881 1.0877 98.75 107.410375 1.18309129 1.0736 100.21 107.585456 1.15261696 1.1235 97.02 109.00197 1.26225225 1.1221 96.48 108.260208 1.25910841 1.1139 95.85 106.767315 1.24077321 1.0995 97.44 107.13528 1.20890025 1.1213 95.66 107.263558 1.25731369 1.1149 96.99 108.134151 1.24300201 1.0779 94.71 102.087909 1.16186841 1.0837 98.66 106.917842 1.17440569 1.1349 95.32 108.178668 1.28799801 1.1621 95.00 110.3995 1.35047641 1.2331 90.65 111.780515 1.52053561 1.2472 88.41 110.264952 1.55550784 1.2672 87.02 110.271744 1.60579584 1.2901 86.05 111.013105 1.66435801 1.3316 82.78 110.229848 1.77315856 1.3539 81.52 110.369928 1.83304521 1.3592 79.81 108.477752 1.84742464 1.3732 80.40 110.40528 1.88567824 1.3812 79.53 109.846836 1.90771344 1.3822 80.25 110.92155 1.91047684 1.3658 79.72 108.881576 1.86540964 1.3610 81.40 110.7854 1.852321 1.3703 80.19 109.884357 1.87772209 1.3492 80.66 108.826472 1.82034064 1.3634 80.26 109.426484 1.85885956 1.3347 80.32 107.203104 1.78142409 1.3309 82.14 109.320126 1.77129481 1.3080 81.54 106.65432 1.710864 1.3188 83.38 109.961544 1.73923344 1.2982 83.40 108.26988 1.68532324 1.3026 81.81 106.565706 1.69676676 1.2963 83.17 107.813271 1.68039369 1.3359 82.00 109.5438 1.78462881 1.3288 79.23 105.280824 1.76570944 1.3119 79.87 104.781453 1.72108161 1.2827 80.16 102.821232 1.64531929 1.2974 79.99 103.779026 1.68324676 1.2855 80.03 102.878565 1.65251025 1.2399 81.22 100.704678 1.53735201 1.2288 82.71 101.634048 1.50994944 1.2526 81.75 102.40005 1.56900676 1.2788 83.13 106.306644 1.63532944

Step 2: Find the sum of every column:

$$\sum{X} = 158.4372 ~,~ \sum{Y} = 9938.49 ~,~ \sum{X \cdot Y} = 13034.299457 ~,~ \sum{X^2} = 210.7573342$$

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{ 9938.49 \cdot 210.7573342 - 158.4372 \cdot 13034.299457}{ 120 \cdot 210.7573342 - 158.4372^2} \approx 156.4 \\ \\b &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 120 \cdot 13034.299457 - 158.4372 \cdot 9938.49 }{ 120 \cdot 210.7573342 - \left( 158.4372 \right)^2} \approx -55.75\end{aligned}

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

\begin{aligned} y~&=~a ~+~ b \cdot x \\y~&=~156.4 ~-~ 55.75 \cdot x\end{aligned}

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Script name : correlation-and-regression-calculator

Form values: 1.1174,1.1311,1.1339,1.1099,1.1092,1.0859,1.0877,1.0736,1.1235,1.1221,1.1139,1.0995,1.1213,1.1149,1.0779,1.0837,1.1349,1.1621,1.2331,1.2472,1.2672,1.2901,1.3316,1.3539,1.3592,1.3732,1.3812,1.3822,1.3658,1.3610,1.3703,1.3492,1.3634,1.3347,1.3309,1.3080,1.3188,1.2982,1.3026,1.2963,1.3359,1.3288,1.3119,1.2827,1.2974,1.2855,1.2399,1.2288,1.2526,1.2788,1.3161,1.3201,1.3224,1.2904,1.3179,1.3555,1.3706,1.3770,1.4343,1.4264,1.4388,1.4348,1.4441,1.3996,1.3648,1.3359,1.3220,1.3660,1.3897,1.3067,1.2894,1.2767,1.2208,1.2565,1.3405,1.3568,1.3685,1.4272,1.4613,1.4911,1.4816,1.4561,1.4268,1.4087,1.4016,1.3650,1.3190,1.3049,1.2784,1.3238,1.3449,1.2732,1.3322,1.4369,1.4975,1.5769,1.5552,1.5557,1.5750,1.5526,1.4748,1.4717,1.4570,1.4683,1.4227,1.3896,1.3622,1.3715,1.3418,1.3511,1.3516,1.3241,1.3074,1.2998,1.3212,1.2881,1.2611,1.2730,1.2811,1.2683 , 95.42,95.88,93.05,94.58,98.22,99.65,98.75,100.21,97.02,96.48,95.85,97.44,95.66,96.99,94.71,98.66,95.32,95.00,90.65,88.41,87.02,86.05,82.78,81.52,79.81,80.40,79.53,80.25,79.72,81.40,80.19,80.66,80.26,80.32,82.14,81.54,83.38,83.40,81.81,83.17,82.00,79.23,79.87,80.16,79.99,80.03,81.22,82.71,81.75,83.13,78.85,79.14,78.79,79.42,80.52,78.49,76.31,79.08,74.17,74.04,74.64,74.70,73.11,76.07,76.92,77.86,79.29,81.27,77.46,78.94,83.25,81.66,86.28,86.67,81.99,81.29,80.44,79.65,78.22,74.94,76.47,76.86,78.22,78.45,80.42,79.43,84.78,85.89,88.15,86.46,82.15,86.70,86.34,79.36,77.50,73.42,72.80,72.95,72.72,72.17,73.75,75.28,76.70,76.17,76.46,77.62,80.75,80.66,81.69,82.25,81.30,82.66,83.50,84.43,83.43,82.85,85.11,85.68,85.02,85.09 , reg

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Correlation and Regression Calculator
Input X and Y values separated by comma or blank space
show help ↓↓ examples ↓↓
Use data grit to input x and y values
 Find the equation of the regression line Find the corelation coefficient
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examples
example 1:ex 1:

Consider the following set of points: ${(-3 , -4), \, (2 , 3), \, (7 , 11)}$

a) Find the regression line for the given data points.

b) Plot the given points and the regression line.

example 2:ex 2:

The values of $X$ and their corresponding values of $Y$ are shown in the table below:

$$\begin{array}{c|ccccc} X & ~1~ & ~2~ & ~3~ & ~4~ & ~5 \\ Y & ~4~ & ~8~ & ~9~ & ~11~& ~16 \end{array}$$

Find a Pearson correlation coefficient.

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