Question

Using the following data...
(a) Fill in the table:

X	Y	X2	Y2	XY
8	5
4	3
9	7
7	6
5	6
ΣX =	ΣY =	ΣX2 =	ΣY2 =	ΣXY =

(b) Compute the degrees of freedom and determine the critical value of r for α = 0.05 (two-tails).

df =
r-critical =  

(c) Compute SS_X, SS_Y, SP, and the Pearson correlation (r). (Use 3 decimals)

SS_X =
SS_Y =
SP =
r =

(d) What decision should be made?

Retain the null.Reject the null.    

(e) Calculate r², the percentage of variance explained: (Use 3 decimals)

r² =

Answer 1

a)

	x	y	x2	y2	xy
	8	5	64	25	40
	4	3	16	9	12
	9	7	81	49	63
	7	6	49	36	42
	5	6	25	36	30
Total	33	27	235	155	187

b)

Degrees of freedom = n - 2 = 5 -2 = 3

α = 0.05 (two-tails)

From the Pearson correlation table, the critical value for α = 0.05 (two-tails) and df =3  is 0.878

i.e df = 3

r-critical = 0.878

c)

Now

d)

Decision rule:

If the computed r value is greater than the r tabular value, reject H0.

In our problem,

Computed value of r = 0.700

Tabulated value of r (r- critical ) = 0.878

Sincde the computed value of r is less than r-critical, there is no enough evidence to reject H0.

So, we fail to reject H0.

Decision: Retain the null

e)

Here,

r = 0.700

So,

r2 = ( 0.700)2 = 0.490

the percentage of variance explained = 49%