$$  $$Listed below are foot lengths​ (mm) and heights​ (mm) of males. Find the regression​ equation, letting foot length be the predictor​ (x) variable. Find the best predicted height of a male with a foot length of 

272.7272.7 

mm. How does the result compare to the actual height of 

17761776 

​mm? Use a significance level of 0.05.

Foot Length

281.8281.8

278.2278.2

253.1253.1

259.0259.0

278.9278.9

258.2258.2

274.0274.0

262.4262.4
 
Height

1785.11785.1

1770.71770.7

1675.71675.7

1645.81645.8

1858.91858.9

1709.81709.8

1788.91788.9

1737.01737.0




The problem statement appears to have formatting issues, particularly in repeating foot length and height values and some missing spacing. I will assume the foot lengths and heights are the same as provided in the initial query. Let’s proceed with the values:

**Foot Lengths (mm):** 281.8, 278.2, 253.1, 259.0, 278.9, 258.2, 274.0, 262.4  
**Heights (mm):** 1785.1, 1770.7, 1675.7, 1645.8, 1858.9, 1709.8, 1788.9, 1737.0

Given the previously calculated regression equation:

\[
\text{Height} = 333.425 + 5.269 \times \text{Foot Length}
\]

We'll use it to find the predicted height for a foot length of 272.7 mm and compare it to the actual height of 1776 mm.

### Predicted Height Calculation

The predicted height for a foot length of 272.7 mm was already calculated as 1770.20 mm.

### Comparison with Actual Height
- **Predicted Height:** 1770.20 mm
- **Actual Height:** 1776 mm

The predicted height is lower than the actual height by approximately 5.80 mm.

### Conclusion
The predicted height, based on the linear regression model, is close to the actual height, indicating a reasonable prediction. However, there is a slight underestimation.

If you have any further questions or need clarification, feel free to ask!

Here are some follow-up questions:
1. How is the correlation coefficient calculated?
2. What is the standard error of the estimate?
3. How does the significance level affect the confidence interval of the regression?
4. What is the coefficient of determination (R²), and what does it signify?
5. How can we check for outliers in the data set?
6. What other variables could improve the accuracy of this predictive model?
7. How would the regression equation change if the foot length were expressed in inches?
8. What is the impact of a higher slope in the regression line?

**Tip:** In regression analysis, always check the residuals (differences between actual and predicted values) to assess the model's accuracy and identify any patterns that may

Learn how to predict male heights based on foot lengths using linear regression. Explore a detailed example with specific data points and comparison of predicted vs actual heights. Suitable for advanced high school students and beyond.

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