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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