Question

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

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 Bone Density 3535 4343 5353 5454 5555 350350 340340 339339 321321 310310

Table

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Step 6 of 6 :

Find the value of the coefficient of determination. Round your answer to three decimal places.

Solution :

 X Y XY X^2 Y^2 35 350 12250 1225 122500 43 340 14620 1849 115600 53 339 17967 2809 114921 54 321 17334 2916 103041 55 310 17050 3025 96100 n 5 sum(XY) 79221 sum(X) 240 sum(Y) 1660 sum(X^2) 11824 sum(Y^2) 552162 Numerator -2295 Denominator 2814.11 r -0.8155 r square 0.6651

The coefficient of determination,

r2 = 0.665

The value of the coefficient of determination is 0.665