Question

Colas per week Bone Mineral Density (grams per cubic centimeter)

0 0.907

0 0.896

1 0.881

1 0.870

2 0.853

2 0.835

2 0.836

3 0.816

4 0.789

5 0.767

5 0.762

6 0.733

7 0.704

7 0.714

7 0.710

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

A) Y with caret = ___x + (___)

B) Interpert the slope ___

C) Interpret the​ y-intercept?

D) Predict the bone mineral density of the femoral neck of a woman who consumes two colas per week.

E) The researchers found a woman who consumed two colas per week to have a bone mineral density of ___g/cm3. this​ woman's bone density above or below average among all women who consume two colas per​ week?

Answer 1

The data provided is shown below:

Colas per week	Bone Mineral Density (grams per cubic centimeter)
0	0.907
0	0.896
1	0.881
1	0.87
2	0.853
2	0.835
2	0.836
3	0.816
4	0.789
5	0.767
5	0.762
6	0.733
7	0.704
7	0.714
7	0.71

The independent variable is X, and the dependent variable is Y. In order to compute the regression coefficients, the following table needs to be used:

	X	Y	X*Y	X2	Y2
	0	0.907	0	0	0.822649
	0	0.896	0	0	0.802816
	1	0.881	0.881	1	0.776161
	1	0.87	0.87	1	0.7569
	2	0.853	1.706	4	0.727609
	2	0.835	1.67	4	0.697225
	2	0.836	1.672	4	0.698896
	3	0.816	2.448	9	0.665856
	4	0.789	3.156	16	0.622521
	5	0.767	3.835	25	0.588289
	5	0.762	3.81	25	0.580644
	6	0.733	4.398	36	0.537289
	7	0.704	4.928	49	0.495616
	7	0.714	4.998	49	0.509796
	7	0.71	4.97	49	0.5041
Sum =	52	12.073	39.342	272	9.786367

Based on the above table, the following is calculated:

Therefore, based on the above calculations, the regression coefficients (the slope m, and the y-intercept n) are obtained as follows:

Therefore, we find that the regression equation is:

Y = 0.8998 - 0.0274 X

B. The slope of -0.0274 is interpreted as follows. As the value of the X variable increases by 1, the value of the Y variable decreases by 0.0274. It is the value by which Y increases for ever unit increase in X.

C.

The y-intercept is the expected mean value of Y when X=0

D.

When X = 2

Y = 0.8998 - 0.0274 * 2 = 0.845

Hence the bone mineral density of the femoral neck of a woman who consumes two colas per week is 0.845 g/cm³

E.

0.845 g/cm³

This​ woman's bone density is above average among all women who consume two colas per​ week.

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