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erica [24]
2 years ago
10

The mean and standard deviation of the number of practices are = 8 practices and sx = 4.47 practices. The mean and standard devi

ation 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.
Mathematics
1 answer:
ddd [48]2 years ago
8 0

Least square regressions are used to find the equation of <em>best fit between two variables</em>.

The equation of the least-squares regression line is: \mathbf{y = 9.414 - 0.213x}

The given parameters are:

\mathbf{\bar x = 8}

\mathbf{\sigma_x = 4.47}

\mathbf{\bar y = 7.71}

\mathbf{\sigma_y = 1.20}

\mathbf{r = -0.793}

The equation of the least-squares regression line is represented as:

\mathbf{y = a + bx}

Where:

\mathbf{b = r \times \frac{\sigma_y}{\sigma_x}}

\mathbf{a = \bar y - b\bar x}

So, we have:

\mathbf{b = r \times \frac{\sigma_y}{\sigma_x}}

\mathbf{b = -0.793 \times \frac{1.20}{4.47}}

\mathbf{b = -0.213}

\mathbf{a = \bar y - b\bar x}

\mathbf{a = 7.71 - (-0.213) \times 8}

\mathbf{a = 9.414}

So, the equation is:

\mathbf{y = a + bx}

\mathbf{y = 9.414 - 0.213x}

Read more about equations of least squares regression at:

brainly.com/question/2141008

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