Question

Can a low barometer reading be used to predict maximum wind speed of an approaching tropical cyclone? For a random sample of tropical cyclones, let *x* be the lowest pressure (in millibars) as a cyclone approaches, and let *y* be the maximum wind speed (in miles per hour) of the cyclone.

x |
1004 | 975 | 992 | 935 | 977 | 924 |

y |
40 | 100 | 65 | 145 | 78 | 153 |

(a) Make a scatter diagram of the data and visualize the line you think best fits the data.

(b) Would you say the correlation is low, moderate, or strong?

Would you say the correlation is positive or negative?

(c) Use a calculator to verify that

x = 5807,

x^{2} = 5,625,235,

y = 581,

y^{2} = 66,343
and

xy = 555,293.

Compute*r*. (Round your answer to three decimal places.)

As*x* increases, does the value of *r* imply that *y* should tend to increase or decrease? Explain your answer.

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(b) Would you say the correlation is low, moderate, or strong?

low

moderate

strong

Would you say the correlation is positive or negative?

positive

negative

(c) Use a calculator to verify that

Compute

As

Given our value of *r*, *y* should tend to increase as *x* increases.

Given our value of *r*, *y* should tend to remain constant as *x* increases.

Given our value of *r*, *y* should tend to decrease as *x* increases.

Given our value of *r*, we can not draw any conclusions for the behavior of *y* as *x* increases.

Step 1

In this question we have the data, using which we have to plot the scatter plot and best line of fit, also we have to explain the type of correlation exists between the variables. Then some measures have been given in the question using which we have to find the correlation by putting the values in the formula.

Step 2

Part A)

The scatter plot and best fit of line.

Step 3

Part B)

The correlation between the variable X and Y seems to be strongly negative, this is simply because as we are increasing the values of X the value of y d...

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