Because colas tend to replace healthier beverages and colas contain caffeine and
ID: 3311885 • Letter: B
Question
Because colas tend to replace healthier beverages and colas contain caffeine and phosphoric acid, researchers wanted to know whether consumption of cola is associated with lower bone mineral density in women. The data shown in the accompanying table represent the typical number of cans of soda consumed in a week and the bone mineral density of the femoral neck for a sample of 15 women. The data were collected through a prospective cohort study. Complete parts (a) through (f).
Number of Colas per Week
(g/cmsquared2)
Number of Colas per Week
(g/cmsquared2)
0
0.897
4
0.873
0
0.882
5
0.875
1
0.891
5
0.871
1
0.877
6
0.867
2
0.888
7
0.862
2
0.871
7
0.872
3
0.868
8
0.865
3
0.876
(d) Predict the bone mineral density of the femoral neck of a woman who consumes four colas per week.
The predicted value of the bone mineral density of the femoral neck of this woman is
??? g/cm2.
(Round to four decimal places as needed.)
Number of Colas per Week
Bone Mineral Density(g/cmsquared2)
Number of Colas per Week
Bone Mineral Density(g/cmsquared2)
0
0.897
4
0.873
0
0.882
5
0.875
1
0.891
5
0.871
1
0.877
6
0.867
2
0.888
7
0.862
2
0.871
7
0.872
3
0.868
8
0.865
3
0.876
Explanation / Answer
Here we need to use regression analysis.
Independent variable (X): Number of Colas per Week
Dependent variables (Y); Bone Mineral Density(g/cmsquared2)
Following is outout of regression analysis generated by excel:
The regression model is
y' = 0.8862 -0.0029x
Putting x = 4 gives the predicted value of the bone mineral density of the femoral neck of this woman is
y' = 0.8862 -0.0029*4 = 0.8746 g/cm2
SUMMARY OUTPUT Regression Statistics Multiple R 0.778354971 R Square 0.605836461 Adjusted R Square 0.575516188 Standard Error 0.006476345 Observations 15 ANOVA df SS MS F Significance F Regression 1 0.000838074 0.000838074 19.98123418 0.00063099 Residual 13 0.00054526 4.1943E-05 Total 14 0.001383333 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 0.886215847 0.00289235 306.3999252 1.79945E-26 0.879967305 0.892464389 X -0.002930328 0.000655549 -4.470037381 0.00063099 -0.004346555 -0.001514101