Bone mineral density and cola consumption has been recorded for a sample of patients

Question

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 = ____-.0022 x + 1.0189____

(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?

Yes/No? __YES___

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

I am using a TI-83+ Calculator and have knowledge of and access to Excel

X Y

2	1.00706
3	1.0146
4	1.01514
5	1.00568
6	1.01422
7	0.99676
8	0.9983
9	1.00284
10	0.99138
11	0.99792
12	1.00146
13	0.98

Answer 1

Hi Anchal,

a. Your regression equation is correct as-is. For scatter plot in TI-83 Plus, plug those data points into the lists L₁ and L₂. Then, enter:

2nd-STAT PLOT (y= button on 83 Plus)

Make sure plot 1 is highlighted.

Scatterplot is Type 1, should be the first mini-graph that appears in the Window.

Make sure x list is L₁, y list is L₂.

Press "graph" to display your scatterplot. I cannot show here due to character limits.

b. For every cola consumed per week, bone density decreases by approximately 0.0022 g/cm³. (I guess I'm in trouble!)

c. To get correlation coefficient from TI-83 Plus, enter: STAT-Calc-LinReg (ax +b). Again, make sure you are using L₁ and L_2. r should appear along with the regression equation.

r= -0.7812

Yes, this is strong correlation. Generally, correlation cutoffs are, by absolute value: 0-0.3=weak, 0.4-0.6=moderate, >=0.7=strong. This meets the strong criterion.

d. Just plug 20 in for x in your regression equation:

y^= -0.022(20) + 1.0189

y^=0.5789 g/cm³

I hope this helps.