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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