Assume that you have paired values consisting of heights (in inches) and weights (in lb) from 40 randomly selected men. The linear correlation coefficient r is 0.464. Find the value of the coefficient of determination. What practical information does the coefficient of determination provide? A.) The coefficient of determination is 0.215. 78.5% of the variation is explained by the linear correlation, and 21.5% is explained by other factors.
B.) The coefficient of determination is 0.785. 21.5% of the variation is explained by the linear correlation, and 78.5% is explained by other factors.
C.) The coefficient of determination is 0.215. 21.5% of the variation is explained by the linear correlation, and 78.5% is explained by other factors.
D.) The coefficient of determination is 0.785. 78.5% of the variation is explained by the linear correlation, and 21.5% is explained by other factors.

C.) The coefficient of determination is 0.215. 21.5% of the variation is explained by the linear correlation, and 78.5% is explained by other factors.

Step-by-step explanation:

Given that :

Number of observations = 40

Linear Correlation Coefficient (R) = 0.464

The Coefficient of determination ( R^2) =?

The Coefficient of determination (R^2) is the squared value of the linear correlation Coefficient value (R) . The value value ranges from 0 to 1 and depicts the proportion of the variation in the dependent variable that can be accounted for by the independent variable.

For the scenario given above,

The Coefficient of determination (R^2) = 0.464^2 = 0.215296 = (0.215296 * 100%) = 21.5%

This means that 21.5% of the variation can be explained by the relationship between both variables while (100% - 21.5% = 78.5%) can be explained by other factors.

proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc

6mm^3 or .6cm^3

      216

      /   \

  36     6

  /   \     /

6     6   6

factor trees are nice.