Question

Step 2 of 5: A study of bone density on 5 random women at a hospital produced the following results. Age Bone Density 48 359 62 350 63 336 63 327 65 319

Calculate the estimated variance of errors, s2ese2. Round your answer to three decimal places.

Answer 1

ΣX = 301
ΣY = 1691
ΣX * Y = 101436
ΣX2 = 18311

Equation of regression line is Ŷ = a + bX
b = ( n Σ(XY) - (ΣX* ΣY) ) / ( n Σ X2 - (ΣX)2 )
b = ( 5 * 101436 - 301 * 1691 ) / ( 5 * 18311 - ( 301 )2)
b = -1.8983

a =( ΣY - ( b * ΣX ) ) / n
a =( 1691 - ( -1.8983 * 301 ) ) / 5
a = 452.479
Equation of regression line becomes Ŷ = 452.479 - 1.8983 X

	Y	Ŷ	( Y - Ŷ)2
	359	361.3595	5.567
	350	334.783	231.557
	336	332.8847	9.705
	327	332.8847	34.630
	319	329.0881	101.769
Total	1691	1691	383.227

Unbiased Estimator of error variance = = Σ (Y - Ŷ )2 / n - 2 = 383.227 / 3 = 127.743