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 WeekBone Mineral Density (g/cm^2)
0 0.893
0 0.884
1 0.891
1 0.877
2 0.888
2 0.871
3 0.868
3 0.876
4 0.873
5 0.875
5 0.871
6 0.867
7 0.862
7 0.872
8 0.865
Critical Values for Correlation Coefficient
n
30.997
40.950
50.878
60.811
70.754
80.707
90.666
100.632
110.602
120.576
130.553
140.532
150.514
160.497
170.482
180.468
190.456
200.444
210.433
220.423
230.413
240.404
250.396
260.388
270.381
280.374
290.367
300.361
n
The least-squares regression line is ^y = -0.0029x + 0.8858
​(b) Interpret the slope.
Select only one option in parenthesis for each.
For each additional cola consumed per​ week, bone mineral density will (decrease, increase) by (0.0029, 1.0054, 0.5423, 0.8858) g/cm2​, on average.
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