Question

I need help with - ​(d) Predict the bone mineral density of the femoral neck of a woman who consumes two colas per week - Thank you!

Because colas tend to replace healthier beverages and colas contain caffeine and phosphoric​ acid, researchers wanted to know whether cola consumption is associated with lower bone mineral density in women. The accompanying data lists the typical number of cans of cola consumed in a week and the femoral neck bone mineral density for a sample of 15 women.

Colas per week   Bone Mineral Density (grams per cubic centimeter)
0   0.907
1   0.871
1   0.882
1   0.873
2   0.858
2   0.841
3   0.816
3   0.823
5   0.772
5   0.777
5   0.773
6   0.747
7   0.719
7   0.730
8   0.701

​(a) Find the​ least-squares regression line treating cola consumption per week as the explanatory variable.

ŷ =−0.025x+(0.900)

​(b) Interpret the slope. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

B.

For every cola consumed per​ week, the bone density decreases by 0.025 g/cm3​, on average.

(c) Interpret the​ y-intercept. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

D

For 0 colas consumed in a​ week, the bone density is predicted to be 0.900 g/cm3.

​(d) Predict the bone mineral density of the femoral neck of a woman who consumes two colas per week.

ŷ =__?__ g/cm3

​(Round to three decimal places as​ needed.)

​

Answer 1

b) Interpretation of slope : For a unit increase in cola consumption per week, the Bone Mineral Density will decrease by 0.025 grams per cubic centimeter.

c) Interpretation of y intercept : When there is no cola consumption per week, the Bone Mineral Density will be 0.9 grams per cubic centimeter.

d) The predicted bone mineral density of the femoral neck of a woman who consumes two colas per week

= 0.9 - (0.025*2)

= 0.85 grams per cubic centimeter