Math Problem Statement

Imagine you are trying to determine the percentage of variation in how many unrestrained motor vehicle deaths there are in a state per 100,000 individuals (a ratio level variable) based on the percentage of the population of the state that have graduated college (a ratio level variable).  Here is the table that has been produced from this data:

What is the coefficient of determination based on this data to three significant digits?

Group of answer choices

-0.562

22.439

0.01

0.318

Imagine you are trying to determine the percentage of variation in how many unrestrained motor vehicle deaths there are in a state per 100,000 individuals (a ratio level variable) based on the percentage of the population of the state that have graduated college (a ratio level variable). What is the coefficient of determination based on this data to three significant digits?

Solution

To determine the coefficient of determination (R2R^2), we start with Pearson's RR value from the table, which is 0.564-0.564. The coefficient of determination is calculated as:

R2=(Pearson’s R)2R^2 = (\text{Pearson's } R)^2

Step-by-Step Calculation:

  1. Pearson's R=0.564R = -0.564
  2. Square the Pearson's RR:
    R2=(0.564)2=0.318R^2 = (-0.564)^2 = 0.318

Thus, the coefficient of determination (R2R^2) is 0.318 to three significant digits.

Correct Answer:

0.318

Let me know if you'd like further details or explanations!

Related Questions:

  1. What does the coefficient of determination (R2R^2) indicate in terms of explained variance?
  2. How is Pearson's RR interpreted for strength and direction of relationships?
  3. What is the difference between Pearson's RR and Spearman's correlation coefficient?
  4. Why is the approximate significance value important in interpreting correlation results?
  5. How does the sample size (50 cases here) affect the reliability of Pearson's RR?

Tip:

The coefficient of determination (R2R^2) shows the proportion of the variance in the dependent variable that is predictable from the independent variable.

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Math Problem Analysis

Mathematical Concepts

Statistics
Correlation Analysis
Coefficient of Determination

Formulas

R^2 = (Pearson's R)^2

Theorems

Concept of Coefficient of Determination (R^2)

Suitable Grade Level

Undergraduate