Question

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. Complete parts​ (a) through​ (f) below.

Find the​ least-squares regression line treating cola consumption per week as the explanatory variable?

colas per week	Bone Mineral Density ​(g/cmcubed3​)
00	0.9070.907
11	0.8750.875
11	0.8880.888
11	0.8770.877
22	0.8660.866
22	0.8500.850
22	0.8490.849
33	0.8370.837
55	0.7960.796
55	0.801

Answer 1

From the given data, the following Table is calculated:

X	Y	XY	X2
0	0.907	0	0
1	0.875	0.875	1
1	0.880	0.88	1
1	0.877	0.877	1
2	0.866	1.732	4
2	0.850	1.7	4
2	0.849	1.698	4
3	0.837	2.511	9
5	0.796	3.98	25
5	0.801	4.005	25
Total = 22	8.538	18.258	74

So,

the​ least-squares regression line treating cola consumption per week as the explanatory variable

is given by:

y = 0.899 - 0.021 x