Plot and describe the distribution of HAV angles among young patients needing surgery for this condition. Provide an appropriate numerical summary. If there are outliers, also obtain the summary statistics omitting them and discuss their influence.Plot and describe the distribution of MA angles among young patients needing surgery for this condition. Provide an appropriate numerical summary. If there are outliers, also obtain the summary statistics omitting them and discuss their influence.Doctors speculate that the severity of MA can help predict the severity of HAV. Make a scatterplot of the data and describe the relationship between MA angle and HAV angle, including any possible outliers. If appropriate, obtain the equation of the least-squares regression line for predicting HAV angle from MA angle.Do the data appear to support the doctors’ speculation? If so, how good a predictor would MA angle be? Provide a numerical measure to support your conclusion. **8.7 A big-toe problem.** Hallux abducto valgus (HAV) is a deformation of the big toe common in youth, often requiring surgery. Metatarsus adductus (MA) is a turning in of the front part of the foot common in adolescents and usually self-correcting. Doctors measure HAV and MA angles of deformity (in degrees) using X-rays in patients under 21 seeking HAV surgery. More pronounced angles imply more serious deformities. ### Table 8.2: Angle of deformity (degrees) for two types of foot deformity| HAV Angle | MA Angle | HAV Angle | MA Angle | HAV Angle | MA Angle ||-----------|----------|-----------|----------|-----------|----------|| 28 | 18 | 21 | 15 | 16 | 10 || 32 | 16 | 17 | 16 | 30 | 12 || 25 | 22 | 16 | 10 | 30 | 10 || 34 | 17 | 21 | 7 | 20 | 10 || 38 | 33 | 23 | 11 | 50 | 12 || 26 | 10 | 14 | 15 | 25 | 25 || 25 | 18 | 32 | 12 | 26 | 30 || 18 | 13 | 25 | 16 | 28 | 22 || 30 | 19 | 21 | 16 | 31 | 24 || 26 | 10 | 22 | 18 | 38 | 20 || 28 | 17 | 20 | 10 | 32 | 37 || 13 | 14 | 18 | 15 | 21 | 23 || 20 | 20 | 26 | 16 | | |### Exercises:a. **HAV Angle Distribution** Plot and describe the distribution of HAV angles among young patients needing

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Plot and describe the distribution of HAV angles among young patients needing surgery for this condition. Provide an appropriate numerical summary. If there are outliers, also obtain the summary statistics omitting them and discuss their influence.
Plot and describe the distribution of MA angles among young patients needing surgery for this condition. Provide an appropriate numerical summary. If there are outliers, also obtain the summary statistics omitting them and discuss their influence.
Doctors speculate that the severity of MA can help predict the severity of HAV. Make a scatterplot of the data and describe the relationship between MA angle and HAV angle, including any possible outliers. If appropriate, obtain the equation of the least-squares regression line for predicting HAV angle from MA angle.
Do the data appear to support the doctors’ speculation? If so, how good a predictor would MA angle be? Provide a numerical measure to support your conclusion.

**8.7 A big-toe problem.** Hallux abducto valgus (HAV) is a deformation of the big toe common in youth, often requiring surgery. Metatarsus adductus (MA) is a turning in of the front part of the foot common in adolescents and usually self-correcting. Doctors measure HAV and MA angles of deformity (in degrees) using X-rays in patients under 21 seeking HAV surgery. More pronounced angles imply more serious deformities.

### Table 8.2: Angle of deformity (degrees) for two types of foot deformity

| HAV Angle | MA Angle | HAV Angle | MA Angle | HAV Angle | MA Angle |
|-----------|----------|-----------|----------|-----------|----------|
| 28 | 18 | 21 | 15 | 16 | 10 |
| 32 | 16 | 17 | 16 | 30 | 12 |
| 25 | 22 | 16 | 10 | 30 | 10 |
| 34 | 17 | 21 | 7 | 20 | 10 |
| 38 | 33 | 23 | 11 | 50 | 12 |
| 26 | 10 | 14 | 15 | 25 | 25 |
| 25 | 18 | 32 | 12 | 26 | 30 |
| 18 | 13 | 25 | 16 | 28 | 22 |
| 30 | 19 | 21 | 16 | 31 | 24 |
| 26 | 10 | 22 | 18 | 38 | 20 |
| 28 | 17 | 20 | 10 | 32 | 37 |
| 13 | 14 | 18 | 15 | 21 | 23 |
| 20 | 20 | 26 | 16 | | |

### Exercises:

a. **HAV Angle Distribution**
Plot and describe the distribution of HAV angles among young patients needing

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