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	40	41	42	43	63
Bone Density	353	344	328	326	322

Step 5

Find the estimated value of y when x=42.

Answer 1

X	Y	XY	X^2	Y^2
40	353	14120	1600	124609
41	344	14104	1681	118336
42	328	13776	1764	107584
43	326	14018	1849	106276
63	322	20286	3969	103684

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

n	5
sum(XY)	76304.00
sum(X)	229.00
sum(Y)	1673.00
sum(X^2)	10863.00
sum(Y^2)	560489.00

b	-0.8522
a	373.6302

ycap = a + bx

ycap = 373.6302 - 0.8522x

when x = 42

Estimated value = 373.6302 - 0.8522 * 42

= 337.84