To determine the correlation coefficient [tex]\( R \)[/tex] between weight and blood sugar levels, we need to figure out the strength and direction of the linear relationship between the two variables.
Given the data:
[tex]\[
\begin{array}{cc}
\text{Weight (lbs)} & \text{Blood Sugar (mg/dL)} \\
128 & 68 \\
154 & 68 \\
202 & 123 \\
222 & 134 \\
103 & 84 \\
\end{array}
\][/tex]
The correlation coefficient [tex]\( R \)[/tex] measures how strongly two variables are related, and its value ranges from -1 to 1:
- [tex]\( R = 1 \)[/tex] implies a perfect positive linear relationship,
- [tex]\( R = -1 \)[/tex] implies a perfect negative linear relationship,
- [tex]\( R = 0 \)[/tex] implies no linear relationship.
After calculating the correlation coefficient using the appropriate statistical methods (such as Pearson's correlation formula or computational tools), we find the value to be approximately 0.8456.
This value is positive and close to 1, indicating a strong positive linear relationship between weight and blood sugar levels. Among the given choices:
- 0.154
- -0.846
- 0.846
- -0.154
The closest value to our computed correlation coefficient [tex]\( 0.8456 \)[/tex] is [tex]\( 0.846 \)[/tex].
Therefore, the approximate value of [tex]\( R \)[/tex] is [tex]\( 0.846 \)[/tex].
