A guidance counselor wants to determine if there is a relationship between a student's number of absences, x, and
1 answer:
The fraction by which the variance of the dependent variable is greater than the variance of the errors is known as R-squared. The correct option is C, 0.32.
<h3>What is R- Squared?</h3>The fraction by which the variance of the dependent variable is greater than the variance of the errors is known as R-squared.
It is called so because it is the square of the correlation between the dependent and independent variables, which is commonly denoted by “r” in a simple regression model.
fraction of the variability in data values = (coefficient of correlation)² = r²
For the given data, the correlation can be found as shown below. Therefore, the value of r is -0.56. Since we need the value of r², the value of r² is,
r² = (-0.56)²
r² = 0.3136 ≈ 0.32
Hence, the correct option is C, 0.32.
Learn more about Correlation Coefficients:
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Answer:
Step-by-step explanation:
Component form of a vector is given by , where
represents change in x-value and
represents change in y-value. The magnitude of a vector is correlated the Pythagorean Theorem. For vector
, the magnitude is
.
190 degrees counterclockwise from the positive x-axis is 10 degrees below the negative x-axis. We can then draw a right triangle 10 degrees below the horizontal with one leg being , one leg being
, and the hypotenuse of the triangle being the magnitude of the vector, which is given as 9.
In any right triangle, the sine/sin of an angle is equal to its opposite side divided by the hypotenuse, or longest side, of the triangle.
Therefore, we have:
To find the other leg, , we can also use basic trigonometry for a right triangle. In right triangles only, the cosine/cos of an angle is equal to its adjacent side divided by the hypotenuse of the triangle. We get:
Verify that
Therefore, the component form of this vector is