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[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

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[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

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Enthusiastic netizens conducted a survey and statistics on the tourism income $y$ (in units of ten thousand yuan) of a popular tourist attraction in Liuzhou City from June to October 2022, and obtained the following data:

| Month $x$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|-----------|-----|-----|-----|-----|------|
| Tourism Income $y$ | $10$ | $12$ | $11$ | $12$ | $20$ |

$(1)$ Based on the data in the table, use the correlation coefficient $r$ to determine whether a linear regression model can be used to fit the relationship between $y$ and $x$. If possible, find the linear regression equation between $y$ and $x$; if not, please explain the reason.

$(2)$ To investigate the evaluation of tourists on the scenic spot, netizens randomly surveyed 200 tourists and obtained the following contingency table. Please fill in the $2\times 2$ contingency table and determine if there is a $99.9\%$ certainty that "whether tourists like the popular tourist attraction is related to gender."

|         | Like | Dislike | Total |
|---------|------|---------|-------|
| Male    |      |         | $100$ |
| Female  |      | $60$    |       |
| Total   | $110$|         |       |

Reference data: $\sqrt{10} \approx 3.162$.

Note: The calculation results of $r$ and $K^{2}$ are accurate to $0.001$. Reference formulas: correlation coefficient $r = \frac{{\sum_{i=1}^n{({{x_i}-\overline{x}})}({{y_i}-\overline{y}})}}{{\sqrt{\sum_i^n{{{({{x_i}-\overline{x}})}^2}}\sum_{i=1}^n{{{({{y_i}-\overline{y}})}^2}}}}$, linear regression equation: $\hat{y} = \hat{b}x + \hat{a}$, where $\hat{b} = \frac{{\sum_{i=1}^n{({{x_i}-\overline{x}})}({{y_i}-\overline{y}})}}{{\sum_{i=1}^n{{{({{x_i}-\overline{x}})}^2}}}}$, $\hat{a} = \overline{y} - \hat{b}\overline{x}$, ${K^2} = \frac{{n{{(ad-bc)}^2}}}{{(a+b)(c+d)(a+c)(b+d)}}$.

Critical value table:

| $P(K^{2}\geqslant k_{0})$ | $0.010$ | $0.005$ | $0.001$ |
|---------------------------|---------|---------|---------|
| $k_{0}$                   | $6.635$| $7.879$| $10.828$|

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