3. This table has data that measures a person's age (in years) and their height (in inches).

Question

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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)

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Answer 1

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.