Question

Bone mineral density and cola consumption has been recorded for a sample of patients. Let represent the number of colas consumed per week and 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.

Y= X +

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

c) Use the linear correlation coefficient to determine if there is correlation. R=

Is there correlation at the 0.05 level of significance?

d) According to the linear regression equation, the bone density of someone who drinks 28 colas per week is

x y

3 0.8631

4 0.873

5 0.8699

6 0.8578

7 0.8547

8 0.8576

9 0.8645

10 0.8674

11 0.8493

12 0.8562

13 0.8561

14 0.85

Answer 1

Regression Analysis: y versus x

The regression equation is
y = 0.8715 - 0.001362 x

S = 0.00607522   R-Sq = 41.8%   R-Sq(adj) = 36.0%

Analysis of Variance

Source      DF         SS         MS     F      P
Regression   1 0.0002654 0.0002654 7.19 0.023
Error       10 0.0003691 0.0000369
Total      11 0.0006344

a)

The regression equation is
y = 0.8715 - 0.001362 x

b)

when the number of colas increase by 1 , bone mineral density decrease by 0.001362 grams

c)

r = 0.646731

p-value = 0.02308 < 0.05

hence there is significant correlation

d)

y^ = 0.8715 - 0.001362 *28

= 0.833364