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

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Basic Math

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.

Age48485151565660606969
Bone Density351351320320318318311311310310

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Step 1 of 6 :

Find the estimatedslope. Round your answer to three decimal places.

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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