Question

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.

Answer 1

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

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:

$\mathbf{y = a + bx}$

$\mathbf{y = 9.414 - 0.213x}$

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