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.

Colas per week   Bone Mineral Density (grams per cubic centimeter)
0   0.907
0   0.896
1   0.880
2   0.842
2   0.851
2   0.835
2   0.835
3   0.814
5   0.757
5   0.762
5   0.758
6   0.729
6   0.727
7   0.709
8   0.676

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

ŷ =__?__x+(__?__)

(Round to three decimal places as​ needed.)

Answer 1

Using Minitab software, (Stat -> Regression -> Regression -> Fit Regression Model), we get the following output :

aMinitab Untitled File Edit Data Calc Stat Graph Editor Tools Window Help Assistant X Q Session Regression Analysis: Bone Mineral Density versus Colas per week Model Summary R-sq (adj) 99.39% R-sq (pred) 99.24% S R-sq 99.43% 0.0056469 Coefficients T-Value Coef SE Coef VIF Term P-Value Constant 0.89996 0.00258 349.32 0.000 -47.75 Colas per week 0.028175 0.000590 0.000 1.00 Regression Equation Bone Mineral Density = 0.89996 -0.028175 Colas per week EWorksheet 1 ** C1 C2 C3 C4 C5 C6 Colas per week Bone Mineral Density 0.907 1 0 0.896 2 1 0.880 3 0.842 2 4 0.851 2 0.835 6 0.835 2 7 3 0.814 8 5 0.757 X Pro. Current Worksheet: Worksheet 1 Type here to search - m un co

a) The least-squares regression line treating cola consumption per week as the explanatory variable is

=0.0282r +0.9