Explore Westonci.ca, the premier Q&A site that helps you find precise answers to your questions, no matter the topic. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
Sagot :
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]
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]
We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.