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, yˆ=b0+b1xy^=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	3535	4343	5353	5454	5555
Bone Density	350350	340340	339339	321321	310310

Table

Copy Data

Step 6 of 6 :  

Find the value of the coefficient of determination. Round your answer to three decimal places.

Answer 1

Solution :

X	Y	XY	X^2	Y^2
35	350	12250	1225	122500
43	340	14620	1849	115600
53	339	17967	2809	114921
54	321	17334	2916	103041
55	310	17050	3025	96100

n	5
sum(XY)	79221.00
sum(X)	240.00
sum(Y)	1660.00
sum(X^2)	11824.00
sum(Y^2)	552162.00
Numerator	-2295.00
Denominator	2814.11
r	-0.8155
r square	0.6651

The coefficient of determination,

r2 = 0.665

Answer :

The value of the coefficient of determination is 0.665