Question

SealChers measured the muscle mass of 16 women (grams per cubic centimeter). The table below shows the results, paired with the age of each woman. The first 15 data pairs are plotted below. 6 Muscle 82 91 Muscle Age 71 120 78 67 100 87 73 60 78 40 56 80 65 80 90 60 70 116 40 50 30 45 76 45 43 49 100 105 100
4· The least squares regression equation that predicts a womans muscle mass from her age is Muscle mass- x AGE 5. On average, how much does a (middle-aged or elderly) womans muscle mass change with each additional year? g/cu cm per year Increase or decrease? 6. Use the least squares line to predict the (average) muscle mass for 62 year old women. 7. Can we use this equation to predict the muscle mass of a 25 year old woman? Why or why not?
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Answer #1

data

age muscle
71 82
64 91
78 77
67 68
56 87
73 73
68 78
56 80
76 65
65 84
45 116
58 76
45 97
43 100
49 105
53 100

excel

data -> data analysis -> regression

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.823894252
R Square 0.678801739
Adjusted R Square 0.655859006
Standard Error 8.343757497
Observations 16
ANOVA
df SS MS F Significance F
Regression 1 2059.781452 2059.781452 29.58678641 8.72099E-05
Residual 14 974.6560483 69.61828917
Total 15 3034.4375
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 148.0506756 11.56292348 12.8039138 4.05142E-09 123.2506712 172.8506799
age -1.023589254 0.188181454 -5.439373715 8.72099E-05 -1.427198332 -0.619980177

4)

muscle = 148.0507 -1.0236 * Age

5)

decrease 1.0236

6)

y^ =

148.0507 -1.0236 * 62

= 84.5875

7)

No, since 25 is not in the range of sample data point

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