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Concept explainers
Foot temperatures: Foot ulcers are a common problem for people with diabetes. Higher skin temperatures on the foot indicate an increased risk of ulcers. In a study carried out at the Colorado School of Mines, skin temperatures on both feet were measured, in degrees Fahrenheit, for 18 diabetic patients. The results are presented in the following table.
- Compute due least-squares regression line for predicting right foot temperature from the left foot temperature.
- Construct a scatter-plot (y) versus the left foot temperature Graph the least-squares regression line on the same axes.
- If the left foot temperatures of two patients differ by 2 degrees: by how much would you predict their right foot temperatures to differ?
- Predict the right foot temperature for a patient whose left foot temperature is 81 degrees.
a.
![Check Mark](/static/check-mark.png)
To find: The least-square regression line for the given data set.
Answer to Problem 25E
The least square regression line of the given data set is,
Explanation of Solution
The foot temperature of both foots are measured of
Calculation:
The least-square regression is given by the formula,
Where
The correlation coefficient is given by the formula,
Supposing the variable
Using the data above, Minitab, the correlation coefficient can be obtained by the following table.
Hence, the correlation coefficient is,
Then, the coefficient
Therefore,
Conclusion:
The least square regression line is found to be,
b.
![Check Mark](/static/check-mark.png)
To graph:The scatter plot for the given data.
Explanation of Solution
Graph:
The scatter plot for the given data can be constructed by considering the temperature of left foot as
Interpretation:
Out of all these
c.
![Check Mark](/static/check-mark.png)
To find:The temperature change of right foot for a change of
Answer to Problem 25E
An increase of
Explanation of Solution
Given:
The least-square regression line has been obtained as
Calculation:
Let
Then the corresponding prediction for the right foot temperature for
Also, for
The second relationship can be simplified as follows.
The difference of these two predicted values gives the change of the right foot temperature for
Conclusion:
Therefore, an increase of
d.
![Check Mark](/static/check-mark.png)
To find: The predicted right foot temperature when the left foot is in
Answer to Problem 25E
The predicted right foot temperature is
Explanation of Solution
Given:
The formula of the least square regression has been determined as
Calculation:
When the temperature of the left foot is
Conclusion:
Therefore, the predicted right foot temperature is
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Chapter 4 Solutions
Elementary Statistics (Text Only)
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