Question

Bone mineral density and cola consumption has been recorded for a sample of patients. Let xx represent the number of colas consumed per week and yy the bone mineral density in grams per cubic centimeter. Based on the data shown below answer the questions rounding your final answers to four decimal places.

(a) Create a scatter plot with linear regression line for the data. (2 points)

y =  x +  

(b) Interpret the slope of the regression equation in a complete sentence. (2 points)



(c) Use the linear correlation coefficient to determine if there is correlation. (5 points)

r =  

Is there correlation at the 0.05 level of significance? (2 points)

yes

no

(d) According to the linear regression equation, the bone density of someone who drinks 26 colas per week is . (2 points)

Submit a file with your scatter plot below. (5 points)

x	y
3	1.0051
4	1.00349
5	1.00988
6	0.99127
7	0.98966
8	0.99005
9	0.98244
10	0.98483
11	0.98422
12	0.98761
13	0.978

Answer 1

(a) a scatter plot with linear regression line for the data.

y=-0.002x+1.013

(b) the slope of the regression equation in a complete sentence.

If x increase by 1 unit then model predicts that y decrease approximately by 0.002

(c) the linear correlation coefficient to determine if there is correlation.

r = -0.8717

  

=-5.34

P value is 0.0005 < 0.05

yes, there is correlation at the 0.05 level of significance.

(d) Substitute x=26 into regression equation

=> y =-0.002*26+1.013

=0.961

the bone density of someone who drinks 26 colas per week is 0.961 grams per cubic centimeter