Claudia records the hours she spent studying and test scores for 5 tests in the table below:
| Hours Spent Studying | Test Score |
| ---------------------- | ---------- |
| 1 | 72 |
| 2 | 80 |
| 3 | 90 |
| 4 | 82 |
| 5 | 95 |
What is the correlation coefficient?
What is the strength of the model?
Answer (2)
Calculate the correlation coefficient: r ≈ 0.847 .
Determine the strength of the model based on the correlation coefficient.
Since 0.7"> ∣ r ∣ > 0.7 , the model has a strong positive correlation.
The correlation coefficient is approximately 0.847, and the strength of the model is strong. 0.847 ; s t ro n g
Explanation
Understanding the Problem First, we need to calculate the correlation coefficient using the given data. The correlation coefficient, denoted as 'r', measures the strength and direction of a linear relationship between two variables. In this case, the variables are the hours spent studying and the test scores.
Calculating the Correlation Coefficient The correlation coefficient (r) has been calculated and is approximately 0.847. This value indicates a strong positive correlation between the hours spent studying and the test scores. A positive correlation means that as the hours spent studying increase, the test scores tend to increase as well.
Determining the Strength of the Model Now, we need to determine the strength of the model based on the correlation coefficient. Since |r| = 0.847, which is greater than 0.7, we can conclude that there is a strong positive correlation.
Final Answer Therefore, the correlation coefficient is approximately 0.847, and the strength of the model is strong.
Examples
Understanding the correlation between study time and test scores can help students optimize their study habits. For example, if a student knows there's a strong positive correlation, they might dedicate more time to studying to improve their grades. This concept extends to other areas, such as analyzing the relationship between exercise and health, or marketing spend and sales revenue. By understanding these correlations, individuals and businesses can make more informed decisions to achieve their goals.
The correlation coefficient is approximately 0.847, indicating a strong positive correlation between hours spent studying and test scores. This suggests that increased study time is associated with higher scores on tests. Hence, the strength of the model is strong.
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