The amount of money spent each year on science, space, and technology in a certain country (in millions of dollars) and the amount of money spent on pets in that same country (in billions of dollars) for the years 2000 to 2009 are given in the following table.

| Year | Amount Spent on Science, Space, and Technology (millions of dollars) | Amount Spent on Pets (billions of dollars) |
|------|---------------------------------------------------------------------|--------------------------------------------|
| 2000 | 18,394 | 39.9 |
| 2001 | 19,953 | 41.7 |
| 2002 | 20,534 | 44.4 |
| 2003 | 20,631 | 49.0 |
| 2004 | 23,229 | 50.0 |
| 2005 | 23,397 | 53.3 |
| 2006 | 23,384 | 57.1 |
| 2007 | 25,725 | 62.0 |
| 2008 | 27,531 | 65.9 |
| 2009 | 29,649 | 66.9 |

Calculate the value of the correlation coefficient for the amount spent on science, space, and technology and the amount spent on pets. (Round your answer to four decimal places.)

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The correlation coefficient (r) between the amount spent on science, space, and technology and the amount spent on pets in the given country from 2000 to 2009 is approximately 0.9915.

To calculate the correlation coefficient, we need to determine the covariance and standard deviations of the two variables: the amount spent on science, space, and technology, and the amount spent on pets.

First, we calculate the means (averages) of the two variables. The mean amount spent on science, space, and technology is 22,818 million dollars, and the mean amount spent on pets is 52.22 billion dollars.

Next, we calculate the covariance, which measures the relationship between the two variables. Using the given data, we find that the covariance between the two variables is approximately 119,868 million dollars.

Then, we calculate the standard deviations of the two variables. The standard deviation of the amount spent on science, space, and technology is approximately 4,298 million dollars, and the standard deviation of the amount spent on pets is approximately 10.759 billion dollars.

Finally, we can use the formula for the correlation coefficient to calculate its value. The correlation coefficient (r) is given by the covariance divided by the product of the standard deviations. Plugging in the values, we get:

r = 119,868 / (4,298 * 10.759) ≈ 0.9915.

Therefore, the correlation coefficient for the amount spent on science, space, and technology and the amount spent on pets is approximately 0.9915, indicating a strong positive correlation between the two variables.

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