Question

How sensitive to changes in water temperature are coral reefs? To find out, scientists examined data on sea surface temperatures and coral growth per year at locations in the Gulf of Mexico and the Caribbean Sea. Scientists examined data on mean sea surface temperatures (in degrees Celsius) and mean coral growth (in centimeters per year) over a several‑year period at locations in the Gulf of Mexico and the Caribbean. The table shows the data for the Gulf of Mexico.
Sea surface temperature 26.7 26.6 26.6 26.5 26.3 26.1
Growth 0.85 0.85 0.79 0.86 0.89 0.92

-Use software to find the mean and standard deviation of both sea surface temperature and growth and then find the correlation between and . Enter your answers in the answer fields using the specific decimal place precision noted.

¯ (rounded to four decimal places)=
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-Use these basic measures to find the equation of the least‑squares line for predicting from . Give the slope and the intercept, rounding both to four decimal places.
slope=
intercept=
-Choose the best explanation that describes in words what the numerical value of the slope tells you.

a) Every increase in coral growth of one centimeter will result in an average of 5.25 fewer degrees Celsius of sea surface temperature per year.

(b) Every increase in coral growth of one centimeter will result in an average of 5.25 more degrees Celsius of sea surface temperature per year.

(c)Every increase in sea surface temperature of one degree Celsius will result in an average of 0.1578 more centimeters of coral growth per year.

(d) Every increase in sea surface temperature of one degree Celsius will result in an average of 0.1578 fewer centimeters of coral growth per year.

Answer 1

The correlation coefficient tells that every increase in sea surface temperature of one degree Celsius will result in an average of 0.1578 fewer centimeters of coral growth per year.

Using technology

The mean= x bar = 26.4667

The mean = y bar= 0.86

The standard deviation= Sx= 0.2251

The standard Deviation Sy=  0.0438

The Correlation Coefficient= r = -0.8111

The slope= b= r* Sy/Sx= -0.15789

The intercept is 5.0389

(d) Every increase in sea surface temperature of one degree Celsius will result in an average of 0.1578 fewer centimeters of coral growth per year.

Here the independent variable is X the sea surface temperature and dependent variable is the Y coral growth.

As the temperature decreases which is along x- axis the growth increases along y axis.

From the given options the option d is the best answer according to the question given.

The same values are calculated using different technology .

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