A guidance counselor wants to determine if there is a relationship between a student's number of absences, x, and
their grade point average (GPA), y. The given data list the number of absences and GPAs for 15 randomly selected
students.
15 1
0 6 9
12
3
3
1
2 7 0 4 9 10
Number of
Absences
GPA
2.1 4.3 4.5 3.2 4.0
1.7
3.8
2.9
3.6
3.4 2.6 3.1 2.8 2.8 4.1
Using technology, what is the value of r²?
O-0.56
O-0.32
O 0.32
O 0.56

Respuesta :

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.

What is R- Squared?

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 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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