Question 1of 2 Step 1 of 00 12 49 The table below gives the age and bone density

Question

Question 1of 2 Step 1 of 00 12 49 The table below gives the age and bone density for five randomly selected women Using this data consider the equation of the regression line y =+ bt for predicting a woman's bone density based on her age. Keep in mind the correlation coefficient may or may not be stambaly 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 35 42 49 54 60 Bone Density 350 334 333 327 323 Table Copy Data Step 1 of 6: Find the estimated slope. Round your answer to three decimal places Prev Points Keypad ch

Explanation / Answer

Line of Regression Y on X i.e Y = bo + b1 X

calculation procedure for regression

mean of X = X / n = 48

mean of Y = Y / n = 333.4

(Xi - Mean)^2 = 386

(Yi - Mean)^2 = 425.2

(Xi-Mean)*(Yi-Mean) = -383

b1 = (Xi-Mean)*(Yi-Mean) / (Xi - Mean)^2

= -383 / 386

= -0.99223

bo = Y / n - b1 * X / n

bo = 333.4 - -0.99223*48 = 381.02694

value of regression equation is, Y = bo + b1 X

Y'=381.02694-0.99223* X

slope = -0.99223

X Y (Xi - Mean)^2 (Yi - Mean)^2 (Xi-Mean)*(Yi-Mean) 35 350 169 275.56 -215.8 42 334 36 0.36 -3.6 49 333 1 0.16 -0.4 54 327 36 40.96 -38.4 60 323 144 108.16 -124.8

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