5.4 Coral Reefs. Exercises 4.2 and 4.10 discuss a study in which scientists exam

Question

5.4 Coral Reefs. Exercises 4.2 and 4.10 discuss a study in which scientists examined data on mean sea surface temperatures (in degrees Celsius) and mean coral growth (in millimeters per year) over a several-year period at locations in the Red Sea. Here are the data:4DATADATACORAL(a) Use your calculator to find the mean and standard deviation of both sea surface temperature x and growth y and the correlation r between x and y. Use these basic measures to find the equation of the least-squares line for predicting y from x.(b) Enter the data into your software or calculator, and use the regression function to find the least-squares line. The result should agree with your work in part (a) up to roundoff error.(c) Say in words what the numerical value of the slope tells you.

Explanation / Answer

sol)

mean(x)=30.26

mean(y)=2.51

sd(x)=0.44

sd(y)=0.15

correlation r=0.899

b)

The Regression equation is

y=a+bx

from Excel

The fitted equation is

y=11.81 -0.31 x)

C)

Slope= -0.31

intercept=11.81

from slope we can say that there is negative correlation between x and y

SUMMARY OUTPUT Regression Statistics Multiple R 0.89864 R Square 0.807554 Adjusted R Square 0.769065 Standard Error 0.07216 Observations 7 ANOVA df SS MS F Significance F Regression 1 0.109251 0.109251 20.98135 0.005945 Residual 5 0.026035 0.005207 Total 6 0.135286 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 11.81085 2.030385 5.817049 0.00212 6.59158 17.03012 Temp -0.3073 0.067089 -4.58054 0.005945 -0.47976 -0.13485

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