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	3939	4747	4848	4949	5252
Bone Density	354354	339339	323323	322322	311311

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
39	354	13806	1521	125316
47	339	15933	2209	114921
48	323	15504	2304	104329
49	322	15778	2401	103684
52	311	16172	2704	96721

n	5
sum(XY)	77193.00
sum(X)	235.00
sum(Y)	1649.00
sum(X^2)	11139.00
sum(Y^2)	544971.00
Numerator	-1550.00
Denominator	1630.15
r	-0.9508
r square	0.9041
Xbar(mean)	47.0000
Ybar(mean)	329.8000
SD(X)	4.3359
SD(Y)	15.0386
b	-3.2979
a	484.8000

r = -0.9508

the value of the coefficient of determination = 0.904