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

Answer:

The slope is m=2.145.

The y-intercept is b=-1.33.

Step-by-step 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:

$m=r\;\dfrac{s_y}{s_x}=0.893\;\dfrac{2.69}{1.12}=2.145$

Then, the y-intercept is calculated as:

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