Experimental data are collected as: x[100]={1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 2

Experimental data are collected as:

x[100]={1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59,
60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78,

79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100};

y[100]={-92.3973,14.0677,98.9626,49.6151,111.88,-38.7967,52.1535,-101.325,65.6111,125.129,151.762, -123.132,-41.8744,-39.3356,-99.7856,-128.881,58.5477,-111.692,-75.3057,4.4723,-100.051,169.051, -15.6953,58.3125,147.346,10.9835,42.3421,166.697,-105.534,-90.2199,151.189,130.022,-8.1448,-51.3493, 164.427,119.154,-99.2704,155.986,133.212,118.035,13.1819,139.678,81.5178,-12.4377,-11.7671,146.627, -25.787,107.25,19.8867,15.6437,112.871,122.552,8.42037,-10.1364,146.682,178.531,203.565,-70.7871, 171.256,-50.6232,193.836,-34.7733,-68.9564,25.3423,75.6537,21.5484,46.5259,-64.22,-13.5792, 74.9213,-26.6872,30.5302,169.534,-36.7224,65.4419,113.978,68.1137,181.414,127.76,145.447,75.5486, 164.201,169.504,110.07,96.713,114.974,155.46,2.72803,-59.9407,13.426,29.9344,-11.052,176.639,

162.505,-18.3784,184.418,234.104,127.227,145.18,0.440172};

Required:
Obtain the regression line in the form of y = a x + b.

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  1. Answer:

    [tex]y = 1.00114x + 1.75243[/tex]

    Step-by-step explanation:

    Given

    The x and y values

    Required

    The regression line equation

    Because of the length of the given data, I will run the analysis using online tools, then analyze the result.

    From the analysis, we have:

    [tex]\sum x = 5050[/tex]

    [tex]\sum y = 5231.1011[/tex]

    [tex]\bar x = 50.5[/tex]

    [tex]\bar y = 52.311[/tex]

    [tex]SSX = 83325[/tex] — Sum of squares

    [tex]SP = 83419.7626[/tex] — Sum of products

    The regression equation is calculated as:

    [tex]y = ax + b[/tex]

    Where:

    [tex]a = \frac{SP}{SSX}[/tex]

    So, we have:

    [tex]a = \frac{83419.76}{83325}[/tex]

    [tex]a = 1.00114[/tex]

    [tex]b = \bar y – a * \bar x[/tex]

    [tex]b = 52.31 – (1.00114*50.5)[/tex]

    [tex]b = 1.75243[/tex]

    So:

    [tex]y = ax + b[/tex] becomes

    [tex]y = 1.00114x + 1.75243[/tex]

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