Lab - Regression & Correlation using SPSS
Homework4 Regression & Correlation using MINITAB
In De Veaux, R. & Velleman, P. “IntroStats’- Addison Wesley, 2003 (page 158) says :
“It is difficult to accurately determine a person’s body fat percentage without immersing him or her in water. Researchers hoping to find ways to make a good estimate immersed 20 male subjects, then measured their waists and recorded their weights’
As described above the purpose of the study is to come up with a model to estimate body fat either in terms of weight or waist that are measurements much easier to make.
You will find the data on the last page of the worksheet that can be copied and pasted into Minitab. Follow the steps and please use software for these questions . There are three variables: Waist (inches), Weight (lb) and Body Fat (%)
1. Use STAT>BASIC STATISTICS>DISPLAY BASIC STATISTICS to calculate mean and standard deviation for the 3 variables. List those values here. (either insert table from output or type or copy values here)
| |Mean |Standard deviation |
|% of Body fat | | |
|waist | | |
|weight | | |
Variable Mean StDev
Waist inches 37.050 3.818
Weight lbs 188.60 26.66
%BodyFat 19.75 9.56
2. Use STAT> BASIC STATISTICS>CORRELATION to calculate the correlation for each pairs of variable, report those values here:
|Correlation between weight and body fat | |
| |Pearson correlation of Weight lbs and %BodyFat = 0.697 |
|Correlation between waist and body fat | |
| |Pearson correlation of Waist inches and %BodyFat = 0.887 |
3. Which is more strongly associated to % of body fat, waist or weight? _______waist_______
4. Pick the variable (waist or weight) that is more strongly related to body fat. Make an scatter plot (GRAPH>PLOT ) for that variable and body fat. Insert the scatter plot here
[pic]
5. Use STAT>REGRESSION>REGRESSION>Fit Regression model to do the regression with ‘body fat’ as response variable and the variable you picked in question 4 as explanatory . Write the equation of the regression line here
Regression Equation
%BodyFat = -62.6 + 2.222 Waist inches
6. Interpret the value of the slope
2.222%/in, For every increase in x, we expect the change in y to be the value of the slope.
7. Interpret the value of R-square
78.65%
This seems like a good fit. Anything over 50% we will say is good
8. Do the regression again but now click on the ‘Storage’ button at the bottom of the Regression window to open a window of options and pick ‘Residuals’ and ‘Fits’
|[pic] |
Look at the Data View of the file, now you will see two new columns there, they are the residuals ([pic]) and the estimated values of body fat ( [pic]) Focus just on the first person in the file and fill on the blanks (this is just to make sure that we understand what each number represents) :
‘Person #1’ ‘s waist is ________ inches
‘Person # 1’ has ________% of body fat
According to the regression model, based on his waist the estimated % of body fat for ‘Person 1’ would be ___________.
For some reason (life style, exercise, etc.) ‘Person # 1’ has ________ % less of body fat from what we would have expected from by just looking at his waist.
(Look carefully at the interpretations, in some other occasion you could be given the values and be asked to interpret them)
Waist inches Weight lbs %BodyFat
32 175 6
36 181 21
38 200 15
33 159 6
39 196 22
40 192 31
41 205 32
35 173 21
38 187 25
38 188 30
33 188 10
40 240 20
36 175 22
32 168 9
44 246 38
33 160 10
41 215 27
34 159 12
34 146 10
44 219 28
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