Respuesta :
Least square regressions are used to find the equation of best fit between two variables.
The equation of the least-squares regression line is: [tex]\mathbf{y = 9.414 - 0.213x}[/tex]
The given parameters are:
[tex]\mathbf{\bar x = 8}[/tex]
[tex]\mathbf{\sigma_x = 4.47}[/tex]
[tex]\mathbf{\bar y = 7.71}[/tex]
[tex]\mathbf{\sigma_y = 1.20}[/tex]
[tex]\mathbf{r = -0.793}[/tex]
The equation of the least-squares regression line is represented as:
[tex]\mathbf{y = a + bx}[/tex]
Where:
[tex]\mathbf{b = r \times \frac{\sigma_y}{\sigma_x}}[/tex]
[tex]\mathbf{a = \bar y - b\bar x}[/tex]
So, we have:
[tex]\mathbf{b = r \times \frac{\sigma_y}{\sigma_x}}[/tex]
[tex]\mathbf{b = -0.793 \times \frac{1.20}{4.47}}[/tex]
[tex]\mathbf{b = -0.213}[/tex]
[tex]\mathbf{a = \bar y - b\bar x}[/tex]
[tex]\mathbf{a = 7.71 - (-0.213) \times 8}[/tex]
[tex]\mathbf{a = 9.414}[/tex]
So, the equation is:
[tex]\mathbf{y = a + bx}[/tex]
[tex]\mathbf{y = 9.414 - 0.213x}[/tex]
Read more about equations of least squares regression at:
https://brainly.com/question/2141008