It is difficult to determine a person’s body fat percentage accurately without immersing him or her in water. Researchers hoping to find ways to make a good estimate immersed 20 male subjects to find their percent body fat and then measured their waists. Their goal is to be able to predict percent body fat from waist size. Waist (in) 32 36 38 33 39 40 41 35 38 38 33 40 36 32 44 33 41 34 34 44 Body Fat (%) 6 21 15 6 22 31 32 21 25 30 10 20 22 9 38 10 27 12 10 28 What is the regression model (i.e. the equation)? What number is the slope in your model? Explain in a complete sentence what the slope of the model means in terms of Waist size and Body Fat. Have Geogebra make a residual plot. What is the purpose of the residual plot? What does the residual plot you made with this data tell you? What is the correlation coefficient r for this data? If you square r, you have R2 – What is your R2 and what does it mean in this context? Use your model to predict the % Body Fat for someone with a waist of 36 inches. Calculate the residual for someone with a waist size of 36 inches and 15% body fat.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
It is difficult to determine a person’s body fat percentage accurately without immersing him or her in water. Researchers hoping to find ways to make a good estimate immersed 20 male subjects to find their percent body fat and then measured their waists. Their goal is to be able to predict percent body fat from waist size.
|
Waist (in) |
32 |
36 |
38 |
33 |
39 |
40 |
41 |
35 |
38 |
38 |
33 |
40 |
36 |
32 |
44 |
33 |
41 |
34 |
34 |
44 |
|
Body Fat (%) |
6 |
21 |
15 |
6 |
22 |
31 |
32 |
21 |
25 |
30 |
10 |
20 |
22 |
9 |
38 |
10 |
27 |
12 |
10 |
28 |
- What is the regression model (i.e. the equation)?
- What number is the slope in your model? Explain in a complete sentence what the slope of the model means in terms of Waist size and Body Fat.
- Have Geogebra make a residual plot. What is the purpose of the residual plot? What does the residual plot you made with this data tell you?
- What is the
correlation coefficient r for this data? If you square r, you have R2 – What is your R2 and what does it mean in this context? - Use your model to predict the % Body Fat for someone with a waist of 36 inches.
- Calculate the residual for someone with a waist size of 36 inches and 15% body fat.
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