Question

The table below gives the age and bone density for five randomly selected women. Using this data, consider the equation of the regression line, y^=b0+b1x, for predicting a woman's bone density based on her age. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant.

Age	39	46	49	56	57
Bone Density	335	329	325	323	319

Step 6

Find the value of the coefficient of determination

Answer 1

X	Y	XY	X^2	Y^2
39	335	13065	1521	112225
46	329	15134	2116	108241
49	325	15925	2401	105625
56	323	18088	3136	104329
57	319	18183	3249	101761

From the above table and formula we get the value are as:

n	5
sum(XY)	80395.00
sum(X)	247.00
sum(Y)	1631.00
sum(X^2)	12423.00
sum(Y^2)	532181.00
Numerator	-882.00
Denominator	907.12
r	-0.9723
r square	0.9454

coefficient of determination = 0.9454