Question

Question 1:

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 29.69 29.86 29.95 30.3 30.51 30.68 30.87

Growth 2.63 2.57 2.62 2.47 2.27 2.37 2.27

Use your calculator to find: The mean (± 0.0001) and standard deviation (± 0.0001) for sea surface temperature: x¯¯¯= sx=

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

Answer 1

Solution:

Performed in R studio:

Sea_surface_temperature_x <- c(29.69, 29.86 ,29.95, 30.3, 30.51, 30.68, 30.87)
mean(Sea_surface_temperature_x)
sd(Sea_surface_temperature_x)
coral_Growth_y <- c(2.63 ,2.57 ,2.62, 2.47, 2.27, 2.37, 2.27)
mean(coral_Growth_y)
sd(coral_Growth_y)
cor(Sea_surface_temperature_x,coral_Growth_y)
regmod <- lm(coral_Growth_y~Sea_surface_temperature_x)
coefficients(regmod)

Output:

> Sea_surface_temperature_x <- c(29.69, 29.86 ,29.95, 30.3, 30.51, 30.68, 30.87)
> mean(Sea_surface_temperature_x)
30.26571
> sd(Sea_surface_temperature_x)
0.4459767
> coral_Growth_y <- c(2.63 ,2.57 ,2.62, 2.47, 2.27, 2.37, 2.27)
> mean(coral_Growth_y)
2.457143
> sd(coral_Growth_y)
0.1564943
> cor(Sea_surface_temperature_x,coral_Growth_y)
[1] -0.9341593
> regmod <- lm(coral_Growth_y~Sea_surface_temperature_x)
> coefficients(regmod)
(Intercept) Sea_surface_temperature_x
12.3782075 -0.3277988

Use your calculator to find: The mean (± 0.0001) and standard deviation (± 0.0001) for sea surface temperature: x¯¯¯= sx=

xbar= 30.26571

Sx=0.44598

ybar=2.45714

Sy=0.15649

r=-0.9342

slope=b=-0.33

y intercept= 12.38