Use the shoe print lengths and heights shown below to find the regression​ equation, letting shoe print lengths be the predictor​ (x) variable. Then find the best predicted height of a male who has a shoe print length of 28.6 cm. Would the result be helpful to police crime scene investigators in trying to describe the​ male? Use a significance level of alphaequals0.05.
 Shoe Print​ (cm)
29.8
29.8
31.6
31.2
27.5
 
 Foot Length​ (cm)
25.7
25.4
27.9
26.7
25.1
 Height​ (cm)
175.6
177.7
185.7
175.6
173.1
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Part 1
What is the regression​ equation?
yequals
  
enter your response hereplus
  
enter your response herex
​(Round to one decimal place as​ needed.)

The regression equation based on the given data is:

\[
y = 113.1 + 2.1x
\]

Where:
- \( y \) is the predicted height in cm.
- \( x \) is the shoe print length in cm.

Now, let's find the best predicted height for a male with a shoe print length of 28.6 cm.The best-predicted height for a male with a shoe print length of 28.6 cm is approximately **174.6 cm**.

### Interpretation for Crime Scene Investigators
This regression result could be somewhat useful to police crime scene investigators as a rough estimate, but it should be noted that the prediction is based on a small sample size, which may not capture all the variability in the population. Additionally, there could be other factors affecting height that are not considered in this model.

### Would you like to delve deeper into any details or have further questions? Here are a few related questions you might consider:

1. How can we assess the accuracy of this regression model?
2. What is the significance level (p-value) of the regression equation, and what does it imply?
3. How does the coefficient of determination \(R^2\) affect the reliability of this prediction?
4. What are the limitations of using linear regression in this context?
5. How could increasing the sample size improve the prediction?

**Tip:** Always consider the context and potential variability in your data when using regression models for predictions.

Use the shoe print lengths and heights shown below to find the regression equation, letting shoe print lengths be the predictor (x) variable. Then find the best-predicted height of a male who has a shoe print length of 28.6 cm. Would the result be helpful to police crime scene investigators in trying to describe the male? Use a significance level of alpha equals 0.05.
Shoe Print (cm):
29.8, 29.8, 31.6, 31.2, 27.5
Foot Length (cm):
25.7, 25.4, 27.9, 26.7, 25.1
Height (cm):
175.6, 177.7, 185.7, 175.6, 173.1

Learn how to find the regression equation for predicting height based on shoe print lengths. This problem involves linear regression and predictive modeling concepts suitable for Grades 11-12 students. Find out how this prediction might assist crime scene investigators.

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