Question

Jaime finished analyzing a set of data with an explanatory variable x and a response variable y. He finds that the mean and standard deviation for x are 5.43 and 1.12, respectively. The mean and standard deviation for y are 10.32 and 2.69, respectively. The correlation was found to be 0.893.

Select the correct slope and y-intercept for the least-squares line.

Answer 1

The slope is m=2.145.

The y-intercept is b=-1.33.

Explanation:

We have this data:

- The mean and standard deviation for x are 5.43 and 1.12, respectively.

- The mean and standard deviation for y are 10.32 and 2.69, respectively.

- The correlation is 0.893.

We have to calculate the slope and the y-intercept of the least-squares line.

With the given data, we can calculate the slope m as:

`m=r\;(s_y)/(s_x)=0.893\;(2.69)/(1.12)=2.145`

Then, the y-intercept is calculated as:

`b=\bar y-m\cdot \bar x=10.32-2.145\cdot 5.43=10.32-11.65=-1.33`