A: (In image) B: fit a quadratic regression model and state the quadratic regression equation C: Predict the mean torque for an RPM of 3,000 D: at the 0.05 level of significance, is there a significant quadratic relationship between torque and RPM? E: what is the test statistic? (F STAT = ___) F: what is the p value? G: adjusted R2 = ___ H: Test statistic (T STAT = ___)

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A: (In image)

B: fit a quadratic regression model and state the quadratic regression equation

C: Predict the mean torque for an RPM of 3,000

D: at the 0.05 level of significance, is there a significant quadratic relationship between torque and RPM?

E: what is the test statistic? (F STAT = ___)

F: what is the p value?

G: adjusted R2 = ___

H: Test statistic (T STAT = ___)

 

RPM    Torque
1500    99.12
1500    97.62
1500    94.34
1500    92.97
1500    98.78
2000    106.37
2000    103.48
2000    104.11
2000    107.91
2000    103.54
2500    109.22
2500    114.27
2500    113.85
2500    110.82
2500    109.96
2660    111.13
2660    115.08
2660    112.02
2660    108.73
2660    119.89
2800    116.83
2800    112.86
2800    113.45
2800    116.76
2800    118.22
2940    116.49
2940    119.19
2940    109.48
2940    116.25
2940    115.16
3500    102.56
3500    108.75
3500    112.16
3500    107.62
3500    109.16
4000    111.20
4000    106.01
4000    105.66
4000    108.28
4000    108.47
4500    101.78
4500    100.43
4500    104.81
4500    106.96
4500    104.66
5000    97.46
5000    99.99
5000    98.15
5000    96.79
5000    93.88
5225    94.88
5225    91.56
5225    96.85
5225    92.68
5225    96.01
5500    86.51
5500    91.69
5500    90.93
5500    90.81
5500    87.41
5775    77.82
5775    78.94
5775    79.88
5775    79.87
5775    79.16
6000    77.13
6000    75.16
6000    75.10
6000    74.72
6000    77.94

**Educational Website Content**

**Title:** Analyzing Engine Speed and Torque

**Introduction:**

A study was conducted on automobile engines to analyze the relationship between engine speed, measured in revolutions per minute (RPM), and engine torque. The aim was to predict engine torque based on RPM. Below are parts of the study, with the first task being to construct a scatter plot for RPM and torque.

**Task a: Construct a scatter plot for RPM and torque.**

**Scatter Plot Options:**

- **Plot A:** Displays a set of data points plotting RPM (0 to 7000) on the x-axis against Torque (60 to 130) on the y-axis. Data points show a downward curve, suggesting torque decreases as RPM increases, then slightly levels off.
  
- **Plot B:** Similar to Plot A, this set shows a strong negative linear relationship, with torque decreasing steadily as RPM increases from 0 to 7000.

- **Plot C:** This plot features an upward trend with torque increasing consistently with RPM. The data forms an upward curve, contrary to a typical negative relation.

- **Plot D:** Displays a U-shaped curve with torque decreasing initially and then sharply increasing as RPM approaches 7000.

### Explanation:
Scatter plots are crucial in visualizing the relationship between two variables. In this study, the objective is to predict engine torque from engine speed, and the correct scatter plot will show a linear or non-linear correlation that can be further analyzed for predictions.

**Conclusion:**

Through constructing and analyzing scatter plots, we can better understand the dynamics between engine speed and torque, leading to more accurate predictions and insights into engine performance.
Transcribed Image Text:**Educational Website Content** **Title:** Analyzing Engine Speed and Torque **Introduction:** A study was conducted on automobile engines to analyze the relationship between engine speed, measured in revolutions per minute (RPM), and engine torque. The aim was to predict engine torque based on RPM. Below are parts of the study, with the first task being to construct a scatter plot for RPM and torque. **Task a: Construct a scatter plot for RPM and torque.** **Scatter Plot Options:** - **Plot A:** Displays a set of data points plotting RPM (0 to 7000) on the x-axis against Torque (60 to 130) on the y-axis. Data points show a downward curve, suggesting torque decreases as RPM increases, then slightly levels off. - **Plot B:** Similar to Plot A, this set shows a strong negative linear relationship, with torque decreasing steadily as RPM increases from 0 to 7000. - **Plot C:** This plot features an upward trend with torque increasing consistently with RPM. The data forms an upward curve, contrary to a typical negative relation. - **Plot D:** Displays a U-shaped curve with torque decreasing initially and then sharply increasing as RPM approaches 7000. ### Explanation: Scatter plots are crucial in visualizing the relationship between two variables. In this study, the objective is to predict engine torque from engine speed, and the correct scatter plot will show a linear or non-linear correlation that can be further analyzed for predictions. **Conclusion:** Through constructing and analyzing scatter plots, we can better understand the dynamics between engine speed and torque, leading to more accurate predictions and insights into engine performance.
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