A data set is given as follows:
Please give the best fit using the least squares with the following functions
(1) y = ax + b;
(2) y = ax + b;
and draw their respective graphs.
(Probability and Statistics)
Answers
Entering the values obtained from the data in the table based on the
given functions of y = a·x + b, and y = a·|x| + b, we have;
(1) y = -0.0614·x + 1.58772
(2) y = 0.3824·x + 0.91168
How can the best fit lines be obtained?The least squares regression formula is presented as follows;
[tex]a = \mathbf{\dfrac{\sum \left(x_i - \bar x\right) \times \left(y_i - \bar y\right) }{\sum \left(x_i - \bar x\right )^2 }}[/tex]
(1) From the data in the table, and by using MS Excel, we have;
[tex]\overline x[/tex] = -0.2
[tex]\overline y[/tex] = 1.6
[tex]\sum \left(x_i - \bar x\right) \times \left(y_i - \bar y\right)[/tex] = -1.4
[tex]\sum \left(x_i - \bar x\right )^2[/tex] = 22.8
Which gives;
[tex]a = \dfrac{-1.4}{22.8 } \approx \mathbf{-0.0614}[/tex]
1.6 ≈ b - 0.0614 × (-0.2)
b = 1.6 - 0.0614 × (0.2) = 1.58772
The equation of best fit for the function, y = a·x + b, is therefore;
y = -0.0614·x + 1.58772(2) For the function, y = a·|x| + b, we have;
[tex]\overline x[/tex] = 1.8
[tex]\overline y[/tex] = 1.6
[tex]\sum \left(x_i - \bar x\right) \times \left(y_i - \bar y\right)[/tex] = 2.6
[tex]\sum \left(x_i - \bar x\right )^2[/tex] = 6.8
Which gives;
[tex]a = \dfrac{2.6}{6.8} \approx \mathbf{0.3824}[/tex]
1.6 ≈ b + 0.3824 × (1.8)
b = 1.6 - 0.3824 × (1.8) = 0.91168
The equation of best fit for the function, y = a·|x| + b, is therefore;
y = 0.3824·x + 0.91168Learn more about the least squares regression line here:
https://brainly.com/question/15882801
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If you want to learn more about probabilities, you can read:
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Answers
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