Question
3. This table has data that measures a person's age (in years) and their height (in inches).
Helpful Resources
Desmos LInk
Directions on how to find the line of best fit (regression line) and r-value using Desmos.
Age (years) Height (inches)
1 29
2 34
3 37
4 40
5 42
6 44
7 47
8 52
9 55
10 60
(1 point)
Part A: The correlation coefficient (r-value) is r =
(Round to the nearest thousandths.)
Part B: The r-value implies that this data has a
correlation. (Write: positive, negative, or no).
Part C: The strength of this correlation is
(Write: strong or weak)
Skip to navigation
Helpful Resources
Desmos LInk
Directions on how to find the line of best fit (regression line) and r-value using Desmos.
Age (years) Height (inches)
1 29
2 34
3 37
4 40
5 42
6 44
7 47
8 52
9 55
10 60
(1 point)
Part A: The correlation coefficient (r-value) is r =
(Round to the nearest thousandths.)
Part B: The r-value implies that this data has a
correlation. (Write: positive, negative, or no).
Part C: The strength of this correlation is
(Write: strong or weak)
Skip to navigation
Answers
GPT-4o mini
To find the correlation coefficient (r-value) and analyze the correlation of the data provided, we can follow these steps:
### Part A: Calculate the r-value
Using the data:
- Age (in years): \(1, 2, 3, 4, 5, 6, 7, 8, 9, 10\)
- Height (in inches): \(29, 34, 37, 40, 42, 44, 47, 52, 55, 60\)
You can input this data into a tool like Desmos to perform a regression analysis. In Desmos, you would input the age and height data, and then use the "LinReg" function to find the line of best fit. This will also give you the correlation coefficient (r-value).
Based on the provided data, after calculating using Desmos or any statistical software, you would find that:
**r ≈ 0.993** (this value is based on typical outputs for linear data like this; please verify with actual calculation).
### Part B: Interpret the r-value
Since the r-value is approximately 0.993, this indicates a strong positive relationship between the age and height. Therefore, the correlation can be described as:
**Positive**
### Part C: Evaluate the strength of the correlation
Based on an r-value of 0.993, we can say that the strength of the correlation is:
**Strong**
### Summary:
- **Part A:** The correlation coefficient (r-value) is **0.993**.
- **Part B:** The r-value implies that this data has a **positive** correlation.
- **Part C:** The strength of this correlation is **strong**.
### Part A: Calculate the r-value
Using the data:
- Age (in years): \(1, 2, 3, 4, 5, 6, 7, 8, 9, 10\)
- Height (in inches): \(29, 34, 37, 40, 42, 44, 47, 52, 55, 60\)
You can input this data into a tool like Desmos to perform a regression analysis. In Desmos, you would input the age and height data, and then use the "LinReg" function to find the line of best fit. This will also give you the correlation coefficient (r-value).
Based on the provided data, after calculating using Desmos or any statistical software, you would find that:
**r ≈ 0.993** (this value is based on typical outputs for linear data like this; please verify with actual calculation).
### Part B: Interpret the r-value
Since the r-value is approximately 0.993, this indicates a strong positive relationship between the age and height. Therefore, the correlation can be described as:
**Positive**
### Part C: Evaluate the strength of the correlation
Based on an r-value of 0.993, we can say that the strength of the correlation is:
**Strong**
### Summary:
- **Part A:** The correlation coefficient (r-value) is **0.993**.
- **Part B:** The r-value implies that this data has a **positive** correlation.
- **Part C:** The strength of this correlation is **strong**.
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