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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