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	37	41	58	61	67
Bone Density	343	330	318	314	312

Step 1 of 6 : Find the estimated slope. Round your answer to three decimal places.

Step 2 of 6: Enter the estimated y-intercept. Round your answer to three decimal places.

Step 3 of 6: Enter the estimated value of y when x=49. Round your answer to three decimal places.

Step 4 of 6: According to the equation for the regression line, if the value of the independent variable is increased by one unit, what is the change in the dependent vairbale y^? (answer choices bo, b1, x, y)

Step 5 of 6: Determine the value of the dependent variable y^ at x=0. (answer choices bo, b1, x, y)

Step 6 of 6: Enter the value of the coefficient of determination. Round your answer to three decimal places.

Answer 1

	Age (X)	Bone Density (Y)	X * Y	X2	Y2
	37	343	12691	1369	117649
	41	330	13530	1681	108900
	58	318	18444	3364	101124
	61	314	19154	3721	98596
	67	312	20904	4489	97344
Total	264	1617	84723	14624	523613

Equation of regression line is Ŷ = a + bX


b = -0.956
a =( Σ Y - ( b * Σ X) ) / n
a =( 1617 - ( -0.9559 * 264 ) ) / 5
a = 373.871
Equation of regression line becomes Ŷ = 373.871 - 0.956 X

Slope b = -0.956

Y intercept =  a = 373.871

When X = 49
Ŷ = 373.871 + -0.956 X
Ŷ = 373.871 + ( -0.956 * 49 )
Ŷ = 327.027

As variable X increases by 1 unit, corresponding change in Y would be - 0.956

When X = 0
Ŷ = 373.871 + -0.956 X
Ŷ = 373.871 + ( -0.956 * 0 )
Ŷ = 373.871

r = -0.963

Coefficient of Determination
R2 = r2 = 0.927