Question

A study is given 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 different locations. Here are the data:

Sea Surface Temperature 29.69 29.87 30.16 30.22 30.48 30.65 30.80
Growth 2.63 2.57 2.67 2.50 2.47 2.38 2.25


Required:
a. Find the mean and standard deviation of both sea surface temperature x and growth y and the correlation r between x and y.
b. Find the least-squares line. The result should agree with your work in part (a) up to roundoff error. (Round your answers to three decimal places.)
c. Say in words what the numerical value of the slope tells you.

Answer 1

Kindly check explanation

Explanation:

Given the following :

Sea Surface Temperature (x) : 29.69 29.87 30.16 30.22 30.48 30.65 30.80

Growth : (y) 2.63 2.57 2.67 2.50 2.47 2.38 2.25

Mean (x) :

Σ(X) / n

n = number of observations

Mean (m1) = Σ(X) / n = 211.87 / 7 = 30.27

Standard deviation(sx) = 0.3742 (using calculator)

Mean (m2) :

Σ(y) / n = 17.47 / 7 = 2.50

Standard deviation(sy) = 0.1354 ( using calculator)

Correlation (r) :

(1/n)Σ[(x - m1) / sx] × [(y - m2) /sy]

Using calculator to save computing time :

r = - 0.8642

b. Find the least-squares line. The result should agree with your work in part (a) up to roundoff error. (Round your answers to three decimal places.)

The least square line using the regression calculator :

y = -0.31 + 11.96x

Comparing to the regression equation format :

y = mx + c

Where ;

-0.31 = intercept ; 11.96 = slope ; x = independent variable ; y = dependent variable

c. Say in words what the numerical value of the slope tells you.

For every 1° degree rise in surface temperature, growth increases by 11.96