Suppose the correlation between height and weight for adults is 0.80. What proportion (or percent) of the variability in weight
1 answer:
Answer: 64% of the variability in weight can be explained by the relationship with height.
Step-by-step explanation:
- In statistics, Correlation coefficient is denoted by 'r' is a measure of the strength of the relationship between two variables.
- Coefficient of determination,
, is a measure of variability in one variable can be explained variation in the other.
Here, r= 0.80
That means 64% of the variability in weight can be explained by the relationship with height.
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Answer: < -4/5, 3/5>
This is equivalent to writing < -0.8, 0.6 >
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Explanation:
Draw an xy grid and plot the point (-4,3) on it. Draw a segment from the origin to this point. Then draw a vertical line until reaching the x axis. See the diagram below.
We have a right triangle with legs of 4 and 3. The hypotenuse is through use of the pythagorean theorem.
We have a 3-4-5 right triangle.
Therefore, the vector is 5 units long. This is the magnitude of the vector.
Divide each component by the magnitude so that the resulting vector is a unit vector pointing in this same direction.
Therefore, we go from < -4, 3 > to < -4/5, 3/5 >
This is equivalent to < -0.8, 0.6 > since -4/5 = -0.8 and 3/5 = 0.6
Side note: Unit vectors are useful in computer graphics.
