
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]


system
A random sample of 10 households was taken from a residential area, and the data on monthly income \( x_i \) (unit: thousand yuan) and monthly savings \( y_i \) (unit: thousand yuan) of the \( i \)-th household were obtained. It is calculated that \( \sum_{i=1}^{10}x_i=80 \), \( \sum_{i=1}^{10}y_i=20 \), \( \sum_{i=1}^{10}x_iy_i=184 \), and \( \sum_{i=1}^{10}x_i^2=720 \).
(1) Find the linear regression equation of household monthly savings \( y \) with respect to monthly income \( x \), with the form \( y=bx+a \).
(2) Determine whether the correlation between variable \( x \) and \( y \) is positive or negative.
(3) If a household in this residential area has a monthly income of 7 thousand yuan, predict the monthly savings of that household.
(Note: For the linear regression equation \( \hat{y}=\hat{b}x+\hat{a} \), where \( \hat{b}=\frac{\sum_{i=1}^{n}x_iy_i-n\overline{x}\overline{y}}{\sum_{i=1}^{n}\overline{x}^2-n\overline{x}^2} \), \( \hat{a}=\overline{y}-\hat{b}\overline{x} \)).

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