Given the following data pairs (x,
y), find the regression equation.[1]
(1, 1.24), (2, 5.23), (3,7.24), (4,
7.60), (5,9.97), (6, 14.31), (7,
13.99), (8, 14.88), (9, 18.04), (10,
20.70)​

Answer:

c

Explanation:

The linear regression equation of the given set of points is required.

The required regression equation is [tex]y=1.98x+0.436[/tex]

The points are

x y       xy                x^2      y^2

1 1.24      1.24           1   1.5376

2 5.23     10.46        4   27.3529

3 7.24     21.72         9   52.4176

4 7.6     30.4             16   57.76

5 9.97     49.85        25   99.4009

6 14.31     85.86        36   204.7761

7 13.99    97.93        49   195.7201

8 14.88    119.04        64   221.4144

9 18.04    162.36       81   325.4416

10 20.7      207          100   428.49

55 113.2   785.86      385   1614.3112 Total

The image of the table is attached.

[tex]\sum y=55[/tex]

[tex]\sum y=113.2[/tex]

[tex]\sum xy=785.86[/tex]

[tex]\sum x^2=385[/tex]

[tex]\sum y^2=1614.3112[/tex]

[tex](\sum x)^2=55\times 55=3025[/tex]

n = Number of observations = 10

The equation of a line is given by

[tex]y=bx+a[/tex]

[tex]a=\dfrac{\left( \sum y \right)\left( \sum {{x}^{2}} \right)-\left( \sum x \right)\left( \sum xy \right)}{n\left( \sum {{x}^{2}} \right)-{{\left( \sum x \right)}^{2}}}\\\Rightarrow a=\dfrac{113.2\times385-55\times785.86}{10\times385-3025}\\\Rightarrow a=0.436[/tex]

[tex]b=\dfrac{n\left( \sum xy \right)-\left( \sum x \right)\left( \sum y \right)}{n\left( \sum {{x}^{2}} \right)-{{\left( \sum x \right)}^{2}}}\\\Rightarrow b=\dfrac{10\times785.86-55\times113.2}{10\times385-3025}\\\Rightarrow b=1.98[/tex]

The required regression equation is [tex]y=1.98x+0.436[/tex]

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