Shelly has saved money since she was 10 years old. She started with $20 and then over the next 10 years the
account grew to $5000. She looked at her history of her savings and calculated he correlation coefficient as 0.85
Which of the following statements could be true? Select all that apply.
There is a strong correlation between Shelly's age and savings.
There is a weak correlation between Shelly's age and savings.
There is a positive correlation between Shelly's age and savings.
There is a negative correlation between Shelly's age and savings.

The sample means are represented with the symbols x(bar) and y(bar), Hence means for Shelly's age (x(bar)) and Money saved (y(bar)) are easily calculated as follows:

x(bar) = (10+20)/2

= 30/2

= 15

y(bar) = (20+5000)/2

= 5020/2

= 2510

Now,

x (xi - x(bar)) y (yi-y(bar))

10 10-15 = -5 20 20-2510 = -2490

20 20-15 = 5 5000 5000-2510 = 2490

∑[(xi - x(bar)) (yi-y(bar))] = (-5)(-2490) + (5)(2490)

= 12450 + 12450

= 24900

Now,

∑[(xi - x(bar))^2]

= (-5)^2 + 5^2

= 25 + 25

= 50

∑[(yi - y(bar))^2]

= (-2490)^2 + 2490^2

= 12400200

Hence,

√[∑[(xi - x(bar))^2] * ∑[(yi - y(bar))^2]]

= √(50 * 12400200)

= √31620510

= 17782.15

Therefore,

r = ∑[(xi - x(bar)) (yi-y(bar))] / √[∑[(xi - x(bar))^2] * ∑[(yi - y(bar))^2]]

r = 24900/17782.15

r = 1.4

But, according to given correlation coefficient (r) = 0.85

The closer r is to zero, the weaker the linear relationship.

Positive r values indicate a positive correlation, where the values of both variables tend to increase together.

Negative r values indicate a negative correlation, where the values of one variable tend to increase when the values of the other variable decrease.

Therefore, There's a strong positive correlation between Shelly's age and savings.

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