have done extensive studies on its increasing tilt. The following table shows how the lean has changed in excess of 2.9 meters by year since 1975. Year Lean Year Line Fit Plot 75 642 780 76 644 77 656 760 667 740 78 79 80 81 673 720 688 700 696 680 82 698 660 83 713 640 84 717 85 725 620 70 75 80 85 90 86 742 87 757 • Lean Predicted Lean Year A regression analysis was run on this data, and the results from Excel are shown below. ANOVA Significance F 0.000000000007 SS MS df 1 15804.48 15804.48 904.1198 Regressior Residual Total 11 192.2857 17.48052 12 15996.77 Upper 95% ower 95.0%Jpper 95.0% -116.4312367 -5.810522 -116.4312 -5.810522 10.0008 8.636565 P-value Lower 95% Intercept Year Coefficientstandard Em t Stat -61.12088 25.12982 -2.432205 0.033279 9.318681 0.309914 30.06858 6.5E-12 8.636564768 10.0008 a) What would Ho and Ha be to show whether the regression line is useful? b) What is the result of the significance test tied to the regression line? Use a = 0.05. SOLVE INTERPRET CLEARLY AND THOROUGHLY. YOU MUST REFERENCE THE CONTEXT OF THE PROBLEM. c) What is the equation of the regression line? (if it in fact exists) Lean

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The Leaning Tower of Pisa is an architectural wonder. Engineers concerned about the tower’s stability have conducted extensive studies on its increasing tilt. The following data shows how the lean has changed, in excess of 2.9 meters, by year since 1975:

| Year | Lean |
|------|------|
| 75   | 642  |
| 76   | 644  |
| 77   | 653  |
| 78   | 667  |
| 79   | 662  |
| 80   | 688  |
| 81   | 698  |
| 82   | 699  |
| 83   | 698  |
| 84   | 717  |
| 85   | 725  |
| 86   | 742  |
| 87   | 757  |

### Graph: Year Line Fit Plot

The graph presents a line fit plot with:
- **X-axis**: Year
- **Y-axis**: Lean
- **Data Points**: Represented with red markers showing the actual measured lean.
- **Line**: A red line indicating the predicted lean based on the regression analysis.

### Regression Analysis Details

Results from Excel’s analysis are as follows:

#### ANOVA Table

- **Regression**: 
  - Degrees of freedom (df): 1
  - Sum of squares (SS): 15804.48
  - Mean square (MS): 15804.48
  - F-statistic: 904.1198
  - Significance F: 0.000000000007

- **Residual**: 
  - Degrees of freedom (df): 11
  - Sum of squares (SS): 192.2857
  - Mean square (MS): 17.48052

- **Total**: 
  - Sum of squares (SS): 15996.77

#### Coefficients

- **Intercept**: -61.12088
- **Standard Error**: 25.12982
- **T-statistic**: -2.432205
- **P-value**: 0.033279
- **Confidence Intervals (95%)**: Lower -116.4312367, Upper -5.810522

- **Year Coefficient**: 9.318681
- **Standard Error**: 0
Transcribed Image Text:The Leaning Tower of Pisa is an architectural wonder. Engineers concerned about the tower’s stability have conducted extensive studies on its increasing tilt. The following data shows how the lean has changed, in excess of 2.9 meters, by year since 1975: | Year | Lean | |------|------| | 75 | 642 | | 76 | 644 | | 77 | 653 | | 78 | 667 | | 79 | 662 | | 80 | 688 | | 81 | 698 | | 82 | 699 | | 83 | 698 | | 84 | 717 | | 85 | 725 | | 86 | 742 | | 87 | 757 | ### Graph: Year Line Fit Plot The graph presents a line fit plot with: - **X-axis**: Year - **Y-axis**: Lean - **Data Points**: Represented with red markers showing the actual measured lean. - **Line**: A red line indicating the predicted lean based on the regression analysis. ### Regression Analysis Details Results from Excel’s analysis are as follows: #### ANOVA Table - **Regression**: - Degrees of freedom (df): 1 - Sum of squares (SS): 15804.48 - Mean square (MS): 15804.48 - F-statistic: 904.1198 - Significance F: 0.000000000007 - **Residual**: - Degrees of freedom (df): 11 - Sum of squares (SS): 192.2857 - Mean square (MS): 17.48052 - **Total**: - Sum of squares (SS): 15996.77 #### Coefficients - **Intercept**: -61.12088 - **Standard Error**: 25.12982 - **T-statistic**: -2.432205 - **P-value**: 0.033279 - **Confidence Intervals (95%)**: Lower -116.4312367, Upper -5.810522 - **Year Coefficient**: 9.318681 - **Standard Error**: 0
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