To address the given problem, we will use the regression equation to predict the tip for a taxi ride that takes 30 minutes and compare this predicted tip to the actual tip of $4.70. Let’s go through the solution step-by-step.
1. Identify the provided regression equation:
The regression equation given is:
[tex]\[
\hat{y} = 24.63 + 0.2467 \times \text{time}
\][/tex]
2. Substitute the specified time (30 minutes) into the regression equation:
[tex]\[
\hat{y} = 24.63 + 0.2467 \times 30
\][/tex]
3. Calculate the predicted tip:
[tex]\[
\hat{y} = 24.63 + (0.2467 \times 30)
\][/tex]
First, multiply the slope (0.2467) by the time (30 minutes):
[tex]\[
0.2467 \times 30 = 7.401
\][/tex]
Then, add this result to the y-intercept (24.63):
[tex]\[
\hat{y} = 24.63 + 7.401 = 32.031
\][/tex]
Thus, the best-predicted tip for a ride that takes 30 minutes is approximately $32.03 when rounded to the nearest cent.
4. Comparison to the actual tip of $4.70:
- The predicted tip is $32.03.
- The actual tip is $4.70.
To decide whether the predicted tip is very different, exactly the same, or close to the actual tip:
- If the predicted tip were exactly $4.70, it would be exactly the same. This is not the case.
- If the predicted tip were within [tex]$0.50 of $[/tex]4.70 (i.e., between [tex]$4.20 and $[/tex]5.20), it would be considered close. This is also not the case.
- Since [tex]$32.03 is far from $[/tex]4.70, we conclude that the best-predicted value is very different from the actual tip of $4.70.
Therefore, the correct comparison according to the given criteria is:
[tex]\[
\boxed{\text{A. The best predicted value is very different from the actual tip of \$4.70.}}
\][/tex]
