(5.03) How sensitive to changes in water temperature are coral reefs? To find ou

Question

(5.03) 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 Red Sea.

Here are the data:

Sea surface temperature   29.66   29.9   30.27   31.18   30.49   30.61   30.89
Growth   2.63   2.58   2.58   2.48   2.27   2.39   2.25

Use your calculator to find:

The mean (±± 0.0001) and standard deviation (±± 0.0001) for sea surface temperature:

x=x¯=
sx=sx=

The mean (±±0.0001) and standard deviation (±± 0.0001) for coral growth:

y=y¯=
sy=sy=

The correlation (±± 0.0001) r =
.

The slope (±± 0.01) of the equation of the least-squares regression line is b =

and the intercept is (±± 0.01) a =

Explanation / Answer

Solution :

Here you have to given data sea surface temp and growth

Using caculator or excel we have to find the mean and sd of both data coloumns.

In excel use this command for mean Average ( drag first coloumn data )

You get mean of sea surface temp =30.476

And using stdev command you get standard deviation =0.465

Similarelly

Mean of growth =2.454

Standard deviation =0.1544

Next find out correlation (r)

using in excel Correl( command you get correlation

r = -0.6073 there is negative correlation between sea surface temp and growth.

Using data analysis tool select regression function in excel enter the both coloumn data values you get this regression equation.

Here slope(b) = -0.20174 and intercept (a) =8.602523.

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 8.602523 3.597372 2.391336 0.062285 -0.64481 17.84986 -0.64481 17.84986 X Variable 1 -0.20174 0.118029 -1.70926 0.148098 -0.50514 0.101661 -0.50514 0.101661

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