Question

3. A set of n = 18 pairs of scores (X and Y values) has SSX = 20, SSY = 80, and SP = 10. If the mean for the X values is MX = 8 and the mean for the Y values is MY = 10. a. Calculate the Pearson correlation for the scores. b. Find the regression equation for predicting Y from the X values. Gravetter, Frederick J. Statistics for The Behavioral Sciences (p. 556). Cengage Learning. Kindle Edition.

Answer 1

Answer:

a. Pearson Correlation

r= $\frac{1}{4}$  or 0,25

b. The regression equation is

$Y = 6+ 0,5 *X$

Step-by-step explanation:

a. Pearson Correlation

Using the equation for Pearson correlation:

$r = \frac{SP}{\sqrt{(SS_{x} * SS_{y})} }$

$r= \frac{10}{\sqrt{(20 * 80)} }$

$r=\frac{10}{\sqrt{1600} }$

$r=\frac{10}{40} =\frac{1}{4} = 0,25$

b. Regression

Using regression equation

1.  $Y = a+ b *X$

2. $a= m_{y} - b* m_{x}$

3. $b= \frac{SP}{SS_{x} }$

So replacing first 'b' because is content in 'a' equation

$b= \frac{SP}{SS_{x} }$

$b= \frac{10}{20}$

$b= \frac{1}{2} = 0,5$

Knowing 'b' can know 'a' and complete the equation

$a= m_{y} - b* m_{x}$

$a= 10 - 0,5* 8$

$a= 6$

Replacing in the equation 1:

1.  $Y = a+ b *X$

$Y = 6+ 0,5 *X$