Question

For a set of data, x is the explanatory variable. Its mean is 8.2, and its standard deviation is 1.92. For the same set of data, y is the response variable. Its mean is 13.8, and its standard deviation is 3.03. The correlation was found to be 0.223.
Select the correct slope and y-intercept for the least-squares line.
a. Slope = -0.35
y-intercept = -10.9
b. Slope = -0.35
y-intercept = 10.9
c. Slope = 0.35
y-intercept = -10.9
d. Slope = 0.35
y-intercept = 10.9

Answer 1

Answer:

d. Slope = 0.35

y-intercept = 10.9

Step-by-step explanation:

The computation is shown below:

Data given in the question

Mean $\bar X$ = 8.2

The standard deviation  of x = $\sigma$ = 1.92

Mean $\bar Y$ = 13.8

The standard deviation  of y = $\sigma$ = 3.03

The correlation = r = 0.223

Based on the above information,

As we know that

The slope is

$b = r \frac{\sigma y }{\sigma x} \\\\ = (0.223) (\frac{3.03}{1.92} \\\\ = (0.223) (1.578125)$

= 0.3519

Now the y-intercept is

$a = \bar Y - b \bar X$

= 13.8  - (0.351922) 8.2

= 13.8 - 2.88579

= 10.91