The mean and standard deviation of the number of practices are = 8 practices and sx = 4.47 practices. The mean and standard deviation of time are = 7.71 minutes and sy = 1.20 minutes. The correlation between number of practices and time to solve the Rubik’s cube is r = –0.793. Find the equation of the least-squares regression line for predicting time to solve the Rubik’s cube from the number of practices.

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

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