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    97.58 1500    99.91 1500    98.44 1500    93.56 1500    97.29 2000    105.61 2000    106.11 2000    105.91 2000    106.41 2000    99.79 2500    112.34 2500    113.67 2500    112.35 2500    112.07 2500    110.92 2660    115.33 2660    115.58 2660    113.60 2660    110.41 2660    116.49 2800    112.67 2800    112.33 2800    110.89 2800    113.90 2800    115.61 2940    116.66 2940    118.04 2940    108.43 2940    115.12 2940    117.11 3500    106.94 3500    107.10 3500    110.54 3500    106.97 3500    109.70 4000    111.75 4000    104.55 4000    105.88 4000    106.10 4000    110.29 4500    104.27 4500    104.36 4500    105.54 4500    104.35 4500    103.83 5000    100.15 5000    97.74 5000    99.02 5000    99.06 5000    98.98 5225    97.63 5225    91.27 5225    94.10 5225    94.98 5225    97.09 5500    86.61 5500    92.61 5500    90.17 5500    88.45 5500    91.37 5775    77.51 5775    79.20 5775    82.67 5775    78.55 5775    79.26 6000    77.04 6000    72.24 6000    71.54 6000    74.69 6000    77.97

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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    97.58
1500    99.91
1500    98.44
1500    93.56
1500    97.29
2000    105.61
2000    106.11
2000    105.91
2000    106.41
2000    99.79
2500    112.34
2500    113.67
2500    112.35
2500    112.07
2500    110.92
2660    115.33
2660    115.58
2660    113.60
2660    110.41
2660    116.49
2800    112.67
2800    112.33
2800    110.89
2800    113.90
2800    115.61
2940    116.66
2940    118.04
2940    108.43
2940    115.12
2940    117.11
3500    106.94
3500    107.10
3500    110.54
3500    106.97
3500    109.70
4000    111.75
4000    104.55
4000    105.88
4000    106.10
4000    110.29
4500    104.27
4500    104.36
4500    105.54
4500    104.35
4500    103.83
5000    100.15
5000    97.74
5000    99.02
5000    99.06
5000    98.98
5225    97.63
5225    91.27
5225    94.10
5225    94.98
5225    97.09
5500    86.61
5500    92.61
5500    90.17
5500    88.45
5500    91.37
5775    77.51
5775    79.20
5775    82.67
5775    78.55
5775    79.26
6000    77.04
6000    72.24
6000    71.54
6000    74.69
6000    77.97

**Title: Analyzing Engine Speed and Torque Relationship**

**Introduction:**

A study was conducted on automobile engines to examine the relationship between engine speed, measured in revolutions per minute (RPM), and engine torque with the goal of predicting engine torque. The data and analysis are structured to enhance understanding of this relationship.

**Task:**

a. Construct a scatter plot for RPM and torque.

**Scatter Plots:**

Four scatter plot options are provided, labeled A, B, C, and D. Each plot presents torque on the vertical axis and RPM on the horizontal axis, with the following observations:

- **Plot A:** Shows a downward trend, indicating that torque decreases as RPM increases.
- **Plot B:** Exhibits a scattering of points without a clear trend.
- **Plot C:** Demonstrates an upward trend, suggesting that torque increases with higher RPM.
- **Plot D:** Illustrates a parabolic pattern where torque initially increases with RPM, reaches a peak, and then decreases.

These visual representations offer insights into how engine speed correlates with torque, aiding in the prediction of engine performance characteristics.
Transcribed Image Text:**Title: Analyzing Engine Speed and Torque Relationship** **Introduction:** A study was conducted on automobile engines to examine the relationship between engine speed, measured in revolutions per minute (RPM), and engine torque with the goal of predicting engine torque. The data and analysis are structured to enhance understanding of this relationship. **Task:** a. Construct a scatter plot for RPM and torque. **Scatter Plots:** Four scatter plot options are provided, labeled A, B, C, and D. Each plot presents torque on the vertical axis and RPM on the horizontal axis, with the following observations: - **Plot A:** Shows a downward trend, indicating that torque decreases as RPM increases. - **Plot B:** Exhibits a scattering of points without a clear trend. - **Plot C:** Demonstrates an upward trend, suggesting that torque increases with higher RPM. - **Plot D:** Illustrates a parabolic pattern where torque initially increases with RPM, reaches a peak, and then decreases. These visual representations offer insights into how engine speed correlates with torque, aiding in the prediction of engine performance characteristics.
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