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

Table

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Step 1 of 6 :

Find the estimated slope. Round your answer to three decimal places.

Answer 1

x	y	(x-x̅)²	(y-ȳ)²	(x-x̅)(y-ȳ)
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

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	284	1610	270.8	1126.0	-422.00
mean	56.80	322.00	SSxx	SSyy	SSxy

sample size ,   n =   5          
here, x̅ = Σx / n=   56.80   ,     ȳ = Σy/n =   322.00  
                  
SSxx =    Σ(x-x̅)² =    270.8000          
SSxy=   Σ(x-x̅)(y-ȳ) =   -422.0          
                  
estimated slope , ß1 = SSxy/SSxx =   -422.0   /   270.800   =   -1.558