
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


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A random sample of $10$ households was taken from a residential area, and the monthly income $x_{i}$ (in thousand yuan) and monthly savings $y_{i}$ (in thousand yuan) of the $i$-th household were obtained. It was calculated that $\sum\limits_{i=1}^{10}x_{i}=80$, $\sum\limits_{i=1}^{10}y_{i}=20$, $\sum\limits_{i=1}^{10}x_{i}y_{i}=184$, $\sum\limits_{i=1}^{10} x _{ i }^{ 2 }=720$. (where $b= \frac { \sum\limits\_{i=1}^{n}x\_{i}y\_{i}-n \overline {x} \overline {y}}{ \sum\limits\_{i=1}^{n} x\_{ i }^{ 2 }-n \overline {x}^{2}}$)

(I) Find the linear regression equation of monthly savings $y$ on monthly income $x$;
(II) Determine whether the variables $x$ and $y$ are positively or negatively correlated;
(III) Predict the monthly savings of a household in this residential area with a monthly income of $7$ thousand yuan.

Present the answer in LaTex format: \boxed{Your answer}
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