MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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### Educational Exercise: Analyzing Foot Lengths and Heights in Males

This exercise involves finding the linear regression equation for a dataset where foot length (in mm) is used as the predictor (independent variable) to estimate the height (in mm) of males. The dataset provided includes foot lengths and corresponding heights:

#### Data Table:
- **Foot Length (mm):** 281.9, 278.1, 253.3, 259.4, 279.1, 257.8, 273.6, 262.2
- **Height (mm):** 1785.0, 1771.2, 1676.2, 1646.2, 1858.9, 1710.2, 1788.7, 1736.6

#### Tasks:
1. **Find the Regression Equation:**
   - The regression equation is of the form:  
     \[
     \hat{y} = ( \text{y-intercept} ) + ( \text{slope} ) \cdot x
     \]
   - Round the y-intercept to the nearest integer and the slope to two decimal places as needed.

2. **Predicting Height:**
   - Compute the best predicted height for a male with a foot length of 273.3 mm.
   - Round the predicted height to the nearest integer.

3. **Comparison to Actual Height:**
   - Compare your predicted height to an actual height of 1776 mm and determine the comparison:
     - **Option A:** The result is very different from the actual height of 1776 mm.
     - **Option B:** The result is exactly the same as the actual height of 1776 mm.
     - **Option C:** The result is close to the actual height of 1776 mm.
     - **Option D:** The result does not make sense given the context of the data.

Consider using statistical software or a calculator to perform the regression analysis to determine the specific values for the y-intercept and slope and to predict the height accurately.
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Transcribed Image Text:### Educational Exercise: Analyzing Foot Lengths and Heights in Males This exercise involves finding the linear regression equation for a dataset where foot length (in mm) is used as the predictor (independent variable) to estimate the height (in mm) of males. The dataset provided includes foot lengths and corresponding heights: #### Data Table: - **Foot Length (mm):** 281.9, 278.1, 253.3, 259.4, 279.1, 257.8, 273.6, 262.2 - **Height (mm):** 1785.0, 1771.2, 1676.2, 1646.2, 1858.9, 1710.2, 1788.7, 1736.6 #### Tasks: 1. **Find the Regression Equation:** - The regression equation is of the form: \[ \hat{y} = ( \text{y-intercept} ) + ( \text{slope} ) \cdot x \] - Round the y-intercept to the nearest integer and the slope to two decimal places as needed. 2. **Predicting Height:** - Compute the best predicted height for a male with a foot length of 273.3 mm. - Round the predicted height to the nearest integer. 3. **Comparison to Actual Height:** - Compare your predicted height to an actual height of 1776 mm and determine the comparison: - **Option A:** The result is very different from the actual height of 1776 mm. - **Option B:** The result is exactly the same as the actual height of 1776 mm. - **Option C:** The result is close to the actual height of 1776 mm. - **Option D:** The result does not make sense given the context of the data. Consider using statistical software or a calculator to perform the regression analysis to determine the specific values for the y-intercept and slope and to predict the height accurately.
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