The scatter chart in the following figure was created using sample data for profits and market capitalizations from the following sample of firms in the Fortune $500.$

Company Profits $($$ millions$)$ Market Capitalization $($$ millions$)$

$1313\mathrm{.}201,901\mathrm{.}90$

$2631\mathrm{.}0081,448\mathrm{.}60$

$3706\mathrm{.}6010,097\mathrm{.}60$

$429\mathrm{.}001,165\mathrm{.}80$

$54,018\mathrm{.}0055,198\mathrm{.}80$

$6959\mathrm{.}0014,125\mathrm{.}20$

$76,490\mathrm{.}0097,366\mathrm{.}20$

$88,572\mathrm{.}00157,120\mathrm{.}50$

$912,436\mathrm{.}0095,241\mathrm{.}90$

$101,462\mathrm{.}0036,471\mathrm{.}20$

$113,461\mathrm{.}0053,585\mathrm{.}70$

$12854\mathrm{.}007,092\mathrm{.}10$

$13369\mathrm{.}503,471\mathrm{.}40$

$14399\mathrm{.}8012,510\mathrm{.}30$

$15278\mathrm{.}003,557\mathrm{.}60$

$169,190\mathrm{.}0032,392\mathrm{.}40$

$17599\mathrm{.}108,915\mathrm{.}30$

$182,465\mathrm{.}009,540\mathrm{.}20$

$193,527\mathrm{.}0065,907\mathrm{.}40$

$20602\mathrm{.}0013,829\mathrm{.}50$

$212,655\mathrm{.}0026,641\mathrm{.}10$

$221,455\mathrm{.}7021,875\mathrm{.}90$

$23276\mathrm{.}003,407\mathrm{.}80$

$24617\mathrm{.}503,671\mathrm{.}20$

$2511,797\mathrm{.}00182,119\mathrm{.}90$

$26567\mathrm{.}6012,532\mathrm{.}80$

$27697\mathrm{.}8010,504\mathrm{.}80$

$28634\mathrm{.}008,570\mathrm{.}50$

$29109\mathrm{.}001,391\mathrm{.}60$

$304,979\mathrm{.}0066,596\mathrm{.}50$

$315,142\mathrm{.}0053,479\mathrm{.}40$

A scatter chart has a horizontal axis labeled "Profits $($millions of $$)"$ with values from $0$ to $16,000$ and a vertical axis labeled "Market Cap $($millions of $$)"$ with values from $0$ to $200,000.$ The scatter chart has $30$ points. A pattern goes up and right from $(100,1,000)$ to $(12,400,182,000).$

$($a$)$

Discuss what the scatter chart indicates about the relationship between profits and market capitalization.

The scatter chart indicates that there is a positive nonlinear relationship between profits and market capitalization.

The scatter chart indicates that there may be a positive linear relationship between profits and market capitalization.

The scatter chart indicates that there may be a negative linear relationship between profits and market capitalization.

The scatter chart indicates that there is no apparent relationship between profits and market capitalization.

The scatter chart indicates that there is a negative nonlinear relationship between profits and market capitalization.

Correct: Your answer is correct.

$($b$)$

Calculate the covariance between profits and market capitalization. $($Round your answer to one decimal place.$)$

$132742057\mathrm{.}4$

Incorrect: Your answer is incorrect.

Discuss what the covariance indicates about the relationship between profits and market capitalization.

The covariance indicates that there is no relationship between profits and market capitalization.

The covariance indicates that there is some positive relationship between profits and market capitalization.

The covariance indicates that there is a strong positive relationship between profits and market capitalization.

The covariance indicates that there is a strong negative relationship between profits and market capitalization.

The covariance indicates that there is some negative relationship between profits and market capitalization.

Correct: Your answer is correct.

$($c$)$

Calculate the correlation coefficient between profits and market capitalization. $($Round your answer to four decimal places.$)$

$0\mathrm{.}8194$

Incorrect: Your answer is incorrect.

What does the correlation coefficient indicate about the relationship between profits and market capitalization?

The correlation coefficient indicates that there is a weak negative relationship between profits and market capitalization.

The correlation coefficient indicates that there is a weak positive relationship between profits and market capitalization.

The correlation coefficient indicates that there is a strong negative relationship between profits and market capitalization.

The correlation coefficient indicates that there is a strong positive relationship between profits and market capitalization.

The correlation coefficient indicates that there is no relationship between profits and market capitalization.

Correct: Your answer is correct.