Question

1). Calculate the specific correlation coefficient for this data. What does r_xy = ? You can use the table on the last page for your calculations (This is the tough one).

2). Does there appear to be a correlation between these two variables? If yes, in what direction (positive or negative)?

3). What are three possible explanations for this correlational relationship? (Note – These can include “third variable” explanations).

Subject #	X	Y	X2	Y2	XY
1	0	9	0	81	0
2	0	7	0	49	0
3	1	6	1	36	6
4	1	7	1	49	7
5	1	8	1	64	8
6	2	5	4	25	10
7	2	6	4	36	12
8	2	7	4	49	14
9	3	3	9	9	9
10	3	4	9	16	12
11	3	5	9	25	15
12	4	3	16	9	12
13	4	4	16	16	16
14	5	3	25	9	15
15	5	4	25	16	20
16	5	5	25	25	25
17	6	5	36	25	30
18	7	4	49	16	28
19	8	4	64	16	32
20	9	3	81	9	27
Σ (Sum)	71	102	379	580	298

X on the graph is the hours spent on social media per day

Y on the graph is the Self-Esteem on a scale of 1-10

Answer 1

The detailed calculation is shown below

Method 1

Method 2 :

Yes there is a negative correlation between the two variable. It is a strong correlation of -0.7357

What do we mean by negative correlation?
Correlation between two variables define the strength and the relationship between two varible.
By strength we mean, how strong or weak is the association between the two variables.

The correlation coefficient takes a value between 0 and 1 and it can have a positive or negative sign depending on the relationship.

Higher the value, stronger is the relationship.
A positive sign indicates that as one variables increase or decreases, the other variable also increase or decreases in the same proportion.

A negative sign indicates that as one variables increases the other decreases and vice versa.

For the last question, we need the context of the question.