Question

WILL GIVE BRAINLY PLEASE HELP!!!!!!!

Answer 1

Answer:

r² = 0.5652  < 0.7 therefore, the correlation between the variables does not imply causation

Step-by-step explanation:

The data points are;

X,          Y

0.7,       1.11

21.9,     3.69

18,         4

16.7,      3.21

18,         3.7

13.8,      1.42

18,          4

13.8,      1.42

15.5,      3.92

16.7,       3.21

The correlation between the values is given by the relation

Y =   b·X + a

$b = \dfrac{N\sum XY - \left (\sum X \right )\left (\sum Y \right )}{N\sum X^{2} - \left (\sum X \right )^{2}}$

$a = \dfrac{\sum Y - b\sum X}{N}$

Where;

N = 10

∑XY = 499.354

∑X = 153.1

∑Y = 29.68

∑Y² = 100.546

∑X² = 2631.01

(∑ X)² = 23439.6

(∑ Y)² = 880.902

From which we have;

$b = \dfrac{10 \times 499.354 -153.1 \times 29.68}{10 \times 2631.01 - 23439.6} = 0.1566$

$a = \dfrac{29.68 - 0.1566 \times 153.1}{10} = 0.5704$

$r = \dfrac{N\sum XY - \left (\sum X \right )\left (\sum Y \right )}{\sqrt{\left [N\sum X^{2} - \left (\sum X \right )^{2} \right ]\times \left [N\sum Y^{2} - \left (\sum Y \right )^{2} \right ]}}$

$r = \dfrac{10 \times 499.354 -153.1 \times 29.68}{\sqrt{\left (10 \times 2631.01 - 23439.6 \right )\times \left (10 \times 100.546- 880.902\right )} } = 0.7518$

r² = 0.5652  which is less than 0.7 therefore, there is a weak relationship between the variables, and it does not imply causation.