The table below gives the age and bone density for five randomly selected women. Using this data,...

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The table below givesthe age and bone density for five randomly selected women. Usingthis data, consider the equation of the regression line,yˆ=b0+b1xy^=b0+b1x, for predicting a woman's bone density based onher age. Keep in mind, the correlation coefficient may or may notbe statistically significant for the data given. Remember, inpractice, it would not be appropriate to use the regression line tomake a prediction if the correlation coefficient is notstatistically significant.
Age 4848 5151 5656 6060 6969
Bone Density 351351 320320 318318 311311 310310
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Step 1 of 6 :
Find the estimatedslope. Round your answer to three decimal places.

Age	4848	5151	5656	6060	6969
Bone Density	351351	320320	318318	311311	310310

Answer & Explanation Solved by verified expert

4.2 Ratings (839 Votes)

x	y	(x-x?)²	(y-y?)²	(x-x?)(y-y?)
48	351	77.44	841.00	-255.20
51	320	33.64	4.00	11.60
56	318	0.64	16.00	3.20
60	311	10.24	121.00	-35.20
69	310	148.84	144.00	-146.40

	?X	?Y	?(x-x?)²	?(y-y?)²	?(x-x?)(y-y?)
total sum	284	1610	270.8	1126.0	-422.00
mean	56.80	322.00	SSxx	SSyy	SSxy

sample size ,   n =   5
here, x? = ?x / n=   56.80   ,     y? = ?y/n =   322.00

SSxx =    ?(x-x?)² =    270.8000
SSxy=   ?(x-x?)(y-y?) =   -422.0

estimated slope , ß1 = SSxy/SSxx =   -422.0   /   270.800   =   -1.558

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