Question

How sensitive to changes in water temperature are coral reefs? To find out, scientists examined data on 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 Sea. The table shows the data for the Gulf of Mexico.

Sea surface temperature	26.726.7	26.626.6	26.626.6	26.526.5	26.326.3	26.126.1
Growth	0.850.85	0.850.85	0.790.79	0.860.86	0.890.89	0.920.92

Find the correlation rr step by step. Round off to two decimals places in each step. First, find the mean and standard deviation of each variable. Then, find the six standardized values for each variable. Finally, use the formula for rr . Round your answer to three decimal places.

Enter these data into your calculator or software, and use the correlation function to find rr . Check that you get the same results as using the formula, up to round off error. Round your answer to three decimal places.

Answer 1

Result:

How sensitive to changes in water temperature are coral reefs? To find out, scientists examined data on 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 Sea. The table shows the data for the Gulf of Mexico.

Sea surface temperature	26.726.7	26.626.6	26.626.6	26.526.5	26.326.3	26.126.1
Growth	0.850.85	0.850.85	0.790.79	0.860.86	0.890.89	0.920.92

Find the correlation rr step by step. Round off to two decimals places in each step. First, find the mean and standard deviation of each variable. Then, find the six standardized values for each variable. Finally, use the formula for r . Round your answer to three decimal places.

Let x= Sea surface temperature and y= Growth

Descriptive statistics
	x	y
count	6	6
mean	26.47	0.86
sample standard deviation	0.23	0.04

x	y	standardized x ( zx)	standardized y (zy)	zx*zy
26.7	0.85	1	-0.25	-0.25
26.6	0.85	0.57	-0.25	-0.1425
26.6	0.79	0.57	-1.75	-0.9975
26.5	0.86	0.13	0.00	0
26.3	0.89	-0.74	0.75	-0.555
26.1	0.92	-1.61	1.50	-2.415
				-4.36

Correlation r = ∑zx*zy/n = -4.36/6 = -0.726666667

= -0.727

Enter these data into your calculator or software, and use the correlation function to find rr . Check that you get the same results as using the formula, up to round off error. Round your answer to three decimal places.

Excel used.

	Sea surface temperature	Growth
Sea surface temperature	1
Growth	-0.811107106	1

Correlation r = -0.811

Due to round off error we get correlation value -0.727 instead of actual correlation value r = -0.811.