Question

Wuestion Help 10- Refer to the accompanying scatterplot a. Examine the pattern of all 10 points and subjectively determine whether there appears to be a strong correlation between x and y. b. Find the value of the correlation coefficient and determine whether there is a linear correlation c. Remove the point with coordinates (2.1) and find the correlation coefficient and determine whether there is a linear correlation. d. What do you conclude about the possible effect from a single pair of values? Click here to view a table of critical values for the correlation coefficient ::: a. Do the data points appear to have a strong linear correlation? Yes Ο Νο 5
please do a, b and c

Answer 1

a)

Yes, why because the point (2,1) is far away from remaining data points

b)

	X	Y
	2	1
	8	8
	8	9
	8	10
	9	8
	9	9
	9	10
	10	8
	10	9
	10	10
Correlation Coefficient (r)	0.892859	CORREL(Xi,Yi)

Hypothesis:

H0​:ρ=0

HA​:ρ̸​=0

df = n−2 = 10−2 = 8

Let α=0.05

rc​ = 0.632

r > rc, reject H0

Therefore, there is enough evidence to conclude that there is a strong linear relationship between X and Y variables

c)

	X	Y
	8	8
	8	9
	8	10
	9	8
	9	9
	9	10
	10	8
	10	9
	10	10
Correlation Coefficient (r)	0	CORREL()

r = 0, which means there is no correlation between X and Y variables

So there is no linear relationship between two variables

Note:

df = n−2 = 9−2 = 7, α=0.05

r < rc = 0.666, Do not reject H0

Therefore, there is not enough evidence to conclude that there is a linear relationship between X and Y variables

d)

"The effect from a single pair of values can change the conclusion"