Question
Use the table to answer the question.
x-value y-value
3 −25
4 −20
5 −15
6 −10
7 −5
8 0
Use the data table to create a scatter plot. Based on the data, which of the following choices would be the best estimated correlation coefficient?
x-value y-value
3 −25
4 −20
5 −15
6 −10
7 −5
8 0
Use the data table to create a scatter plot. Based on the data, which of the following choices would be the best estimated correlation coefficient?
Answers
GPT-4o mini
To determine the best estimated correlation coefficient based on the data provided, we first need to analyze the relationship between the x-values and the y-values given in the table:
\[
\begin{array}{|c|c|}
\hline
\text{x-value} & \text{y-value} \\
\hline
3 & -25 \\
4 & -20 \\
5 & -15 \\
6 & -10 \\
7 & -5 \\
8 & 0 \\
\hline
\end{array}
\]
From the table, as the x-values increase from 3 to 8, the y-values increase from -25 to 0. This indicates a positive correlation between the x and y values, as the y-value becomes less negative (increases) with increasing x.
### Steps to Estimate the Correlation Coefficient:
1. **Identify the Pattern**: The values clearly show a trend where increases in x result in increases in y.
2. **Direction of the Correlation**: The correlation is positive since higher x-values correspond to higher y-values.
3. **Strength of the Correlation**: The increments in y are consistent as x increases by 1. From -25 to 0 over 5 steps (from x=3 to x=8), the change in y is from -25 to 0, which indicates a strong linear relationship.
### Estimation:
- A correlation coefficient (r) of +1 would indicate a perfect positive linear relationship.
- A correlation coefficient closer to +1 (like +0.9 or +0.8) indicates a strong positive relationship but not perfect.
- Given that there’s a clear, consistent increase, the correlation coefficient is likely to be close to +1.
### Best Estimated Correlation Coefficient:
Based on this analysis, the best estimated correlation coefficient for the given data would be **around +0.9** (indicative of a strong positive correlation).
If you have specific choices, I'd recommend selecting the one that is closest to +0.9 if that is an option. If the closest option is +1.0, that would also be acceptable because the relationship appears very strong.
\[
\begin{array}{|c|c|}
\hline
\text{x-value} & \text{y-value} \\
\hline
3 & -25 \\
4 & -20 \\
5 & -15 \\
6 & -10 \\
7 & -5 \\
8 & 0 \\
\hline
\end{array}
\]
From the table, as the x-values increase from 3 to 8, the y-values increase from -25 to 0. This indicates a positive correlation between the x and y values, as the y-value becomes less negative (increases) with increasing x.
### Steps to Estimate the Correlation Coefficient:
1. **Identify the Pattern**: The values clearly show a trend where increases in x result in increases in y.
2. **Direction of the Correlation**: The correlation is positive since higher x-values correspond to higher y-values.
3. **Strength of the Correlation**: The increments in y are consistent as x increases by 1. From -25 to 0 over 5 steps (from x=3 to x=8), the change in y is from -25 to 0, which indicates a strong linear relationship.
### Estimation:
- A correlation coefficient (r) of +1 would indicate a perfect positive linear relationship.
- A correlation coefficient closer to +1 (like +0.9 or +0.8) indicates a strong positive relationship but not perfect.
- Given that there’s a clear, consistent increase, the correlation coefficient is likely to be close to +1.
### Best Estimated Correlation Coefficient:
Based on this analysis, the best estimated correlation coefficient for the given data would be **around +0.9** (indicative of a strong positive correlation).
If you have specific choices, I'd recommend selecting the one that is closest to +0.9 if that is an option. If the closest option is +1.0, that would also be acceptable because the relationship appears very strong.