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.

Kindly check explanation

Step-by-step 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

b because it contains 40% of the possible results from the random list.  

0,1,2,3 v 4,5,6,7,8,9  

4 integers to 6 integers  

40% success vs 60% fail

step-by-step explanation:

answer:   the paragraph proof is mentioned below.

step-by-step explanation:

given: in a δxwy where

such that, ∠wzx ≅ ∠yzx and zw≅zy

we have to prove that: segment zx is a perpendicular bisector of segment wy.

prove: since, zw≅zy ⇒ ∠wzy is a supplementary angle.

then, ∠wzy= 180°

⇒∠wzx + ∠yzx = 180° ( because xz divides ∠wzy into two parts)

but, ∠wzx ≅ ∠yzx ( given)

⇒∠wzy+∠wzy=180° ( by substitution)

⇒2∠wzy=180°

⇒∠wzy=90°

⇒∠wzy=∠yzx =90°

therefore, xz⊥wy where wz=zy

⇒zx is a perpendicular bisector of wy.