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Which equation of the least squares regression line most closely matches the data set?



yˆ=−0.31x+37.3


yˆ=−0.09x+11.5


yˆ=−10.1x+118.8


yˆ=−2.3x+97.9

Which equation of the least squares regression line most closely matches the data set yˆ 0 31x 37 3 yˆ 0 09x 11 5 yˆ

Answer :

The equation of the least squares regression line which is most closely matches the data set is yˆ=−10.1x+118.8

What is linear regression?

Linear regression is a type of regression which is used to model the data having linear relationship between the variables. The regression line can be given as,

[tex]\hat y=bX+a[/tex]

The data given in the problem is,

  • x 2 4 6 8 10
  • y 100 83 50 35 23

Mean of x and y values,

[tex]\mu_x=\dfrac{2 +4 +6 +8 +10}{5}=6\\\mu_y=\dfrac{100 +83 +50 +35 +23}{5}=58.2[/tex]

Here, in this data points, the sum of the squares is 40 and sum of the products is -404. The value of b is,

[tex]b=\dfrac{-404}{40}\\b=-10.1[/tex]

The value of a is,

[tex]a=58.2-(10.1\times6)\\a=118.8[/tex]

Put the values in the above equation,

[tex]\hat y=-10.1X+118.8a[/tex]

Thus, the equation of the least squares regression line which is most closely matches the data set is yˆ=−10.1x+118.8

Learn more about the linear regression here;

https://brainly.com/question/25226042

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Answer:

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