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

Click on the datafile logo to reference the data.

The datafile logo$.$

A scatter chart of market capitalization versus profits displays the data from the Data file. The horizontal axis is labeled Profits $($millions of dollars$)$ with values from $0$ to $16000$ and the vertical axis is labeled Market Cap $($millions of dollars$)$ with values from $0$ to $200000.$ Each point on the chart represents one company from the data set. Most of the points on the graph are in the area from $0$ to $4000$ million profit on the horizontal axis and from $0$ to $80000$ million capital on the vertical axis. The other points are as follows: $4018$ million profit and $55189$ million capital, $4979$ million profit and $66607$ million capital, $5142$ million profit and $53469$ million capital, $6490$ million profit and $97376$ million capital, $8572$ million profit and $157131$ million capital, $9190$ million profit and $32382$ million capital, $11797$ million profit and $182110$ million capital, and $12436$ million profit and $95252$ million capital.

$($a$)$ Discuss what does this scatter chart indicate about the relationship between profits and market capitalization?

The scatter chart indicate that there may be a

positive

linear relationship between profits and market capitalization.

$($b$)$ The data used to produce this are contained in the file Fortune$500.$ Calculate the covariance between profits and market capitalization.

If required, round your answer to an integer. If your answer is negative use $$minus sign.$$

Discuss what does the covariance indicate about the relationship between profits and market capitalization?

This indicates that there is a

$-$ Select your answer $-$

relationship between profits and market capitalization.

$($c$)$ Calculate the correlation coefficient between profits and market capitalization.

If required, round your answer to four decimal places. If your answer is negative use $$minus sign.$$

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

This indicates that there is a

$-$ Select your answer $-$

between profits and market capitalization.