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In recent years, under the shortage of "core" components, the call for domestic substitutes has been increasing. With the support of national policies, domestic chip manufacturers have experienced explosive growth. To estimate the operating income of a chip company in a certain area, data from $10$ chip companies were randomly selected, and the research and development investment (unit: billion) and operating income (unit: billion) of each company were recorded as follows:

| Sample $i$ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|------------|---|---|---|---|---|---|---|---|---|----|
| R&D Investment $x_{i}$ | 2 | 2 | 4 | 6 | 8 | 10 | 14 | 16 | 18 | 20 |
| Operating Income $y_{i}$ | 14 | 16 | 30 | 38 | 50 | 60 | 70 | 90 | 102 | 130 |

It was calculated that $\sum_{i=1}^{10}{{x_i}}=100$, $\sum_{i=1}^{10}{{y_i}}=600$, $\sum_{i=1}^{10}{x_i^2}=1400$, $\sum_{i=1}^{10}{y_i^2}=49200$, and $\sum_{i=1}^{10}{{x_i}{y_i}}=8264$.

$(1)$ Calculate the sample correlation coefficient $r$ between the research and development investment and operating income of the chip companies in this area. Determine the strength of the correlation between these two variables (if $0.30\leqslant |r| \lt 0.75$, the linear correlation is moderate; if $|r|\geqslant 0.75$, the linear correlation is strong. Round $r$ to $0.01$).

$(2)$ Now, the total research and development investment of all chip companies in this area is $268$ billion. It is known that the research and development investment of chip companies is approximately proportional to their operating income. Use the given data to provide an estimate of the total operating income of chip companies in this area.

Given: The correlation coefficient $r=\frac{{\sum_{i=1}^n{({{x_i}-\overline{x}})}({{y_i}-\overline{y}})}}{{\sqrt{\sum_{i=1}^n{{{({{x_i}-\overline{x}})}^2}\sum_{i=1}^n{{{({{y_i}-\overline{y}})}^2}}}}}}$, $\sqrt{33}≈5.745$.

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