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+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 50 59 60 64 68 Bone Density 331 326 325 320 315 Table Step 6 of 6 : Find the value of the coefficient of determination. Round your answer to three decimal places.

Answer 1

Step 6. First we will find correlation coefficient

X Values
∑ = 301
Mean = 60.2
∑(X - M_x)² = SS_x = 180.8

Y Values
∑ = 1617
Mean = 323.4
∑(Y - M_y)² = SS_y = 149.2

X and Y Combined
N = 5
∑(X - M_x)(Y - M_y) = -159.4

R Calculation
r = ∑((X - M_y)(Y - M_x)) / √((SS_x)(SS_y))

r = -159.4 / √((180.8)(149.2)) = -0.971

So r^2=0.943