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;
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