To determine the best predicted productivity score for an individual whose dexterity score is 32, you need to use the given regression equation:
[tex]\[ \hat{y} = 5.50 + 1.91x \][/tex]
Here, [tex]\( x \)[/tex] is the dexterity score. Let's go through the calculation step-by-step.
1. Identify the values:
- Intercept [tex]\( b_0 = 5.50 \)[/tex]
- Slope [tex]\( b_1 = 1.91 \)[/tex]
- Dexterity score [tex]\( x = 32 \)[/tex]
2. Insert the known values into the regression equation:
[tex]\[
\hat{y} = 5.50 + 1.91 \cdot x
\][/tex]
3. Substitute [tex]\( x \)[/tex] with 32:
[tex]\[
\hat{y} = 5.50 + 1.91 \cdot 32
\][/tex]
4. Perform the multiplication and addition:
[tex]\[
\hat{y} = 5.50 + 61.12
\][/tex]
5. Add the two numbers together to get the predicted productivity score:
[tex]\[
\hat{y} = 66.62
\][/tex]
Therefore, the best predicted productivity score for a person whose dexterity score is 32 is:
[tex]\[ \boxed{66.62} \][/tex]
