Question

A hospital analyzed the relationship between the distance an employee must travel between home and work (in 10s of miles) and the annual number of unauthorized work absences (in days) for several randomly selected hospital employees. The regression analysis showed df_Err = 15, SS_xx = 23.88, SS_yy = 130.00, and SS_xy = -54.50.

What is the 99% confidence interval for β₁ (with appropriate units)?

	a.	(-0.2651 days/mile, -0.1913 days/mile)
	b.	(-2.6081 days, -1.9564 days)
	c.	(-26.5130 days/mile, -19.1319 days/mile)
	d.	None of the answers is correct
	e.	(-2.6513 days, -1.9132 days)

Answer 1

= SSxy/SSxx =-54.50/23.88 = - 2.2822

Sum Square Regression, SSR = *SSxy =2.2822*54.5 = 124.3799

Sum Square Error = SSyy-SSR = 130-124.3799 =5.6201

DFerror=15

Mean Square Error, = MSE=SSE/ DFerror =5.6201/15 = 0.3747

SE (​​​​​​) ^2 = /SSxx =0.3747 / 23.88 = 0.0157

SE (​​​​​​) = 0.1253

99% confidence interval for is

- t/2=0.005,15 *SE(​​​​​​) ,   + t/2=0.005,15 * SE(​​​​​​)

=-2.2822 - 2.947 * 0.1253 , - 2.2822+ 2.947 * 0.1253

= - 2.2822 - 0.3693, - 2.2822 +0.3693

= - 2.6515, - 1.9129

So, correct answer would be -2.6515 days/mile to - 1.9129 days per mile.

Option e would be right but unit is wrong. (neglecting roundoff error)

So, option d is correct.

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