Question

Use the Excel output in the below table to do (1) through (6) for each ofβ₀, β₁, β₂, and β₃.

y = β₀ + β₁x₁ + β₂x₂ + β₃x₃ + ε     df = n – (k + 1) = 16 – (3 + 1) = 12

Excel output for the hospital labor needs case (sample size: n = 16)

	Coefficients	Standard Error	t Stat	p-value	Lower 95%	Upper 95%
Intercept	1946.8020	504.1819	3.8613	0.0023	848.2840	3045.3201
XRay (x1)	0.0386	0.0130	2.9579	0.0120	0.0102	0.0670
BedDays(x2)	1.0394	0.0676	15.3857	2.91E-09	0.8922	1.1866
LengthSt(x3)	-413.7578	98.5983	-4.1964	0.0012	-628.5850	-198.9306

(1) Find b_j, sb_j, and the t statistic for testing H₀: β_j = 0 on the output and report their values. (Round your t value answers to 3 decimal places and other answers to 4 decimal places.)

	bj	sbj	t
H0: β0 = 0
H0: β1 = 0
H0: β2 = 0
H0: β3 = 0

(2) Using the t statistic and appropriate critical values, test H₀: β_j = 0 versus H_a: β_j ≠ 0 by setting α equal to .05. Which independent variables are significantly related to y in the model with α = .05? (Round your answer to 3 decimal places.)

t_.025                             

H0: β0 = 0;	(Click to select)Do not rejectReject H0
H0: β1 = 0;	(Click to select)Do not rejectReject H0
H0: β2 = 0;	(Click to select)RejectDo not reject H0
H0: β3 = 0;	(Click to select)Do not rejectReject H0

(3) Using the t statistic and appropriate critical values, test H₀: β_j = 0 versus H_a: β_j ≠ 0 by setting α equal to .01. Which independent variables are significantly related to y in the model with α = .01? (Round your answer to 3 decimal places.)

t_.005                          

H0: β0 = 0;	(Click to select)Do not rejectReject H0
H0: β1 = 0;	(Click to select)RejectDo not reject H0
H0: β2 = 0;	(Click to select)RejectDo not reject H0
H0: β3 = 0;	(Click to select)Do not rejectReject H0

(4) Find the p-value for testing H₀: β_j = 0 versus H_a: β_j ≠ 0 on the output. Using the p-value, determine whether we can reject H₀ by setting α equal to .10, .05, .01, and .001. What do you conclude about the significance of the independent variables in the model? (Round your answers to p-value at β ₂ = 0 and β₃ = 0 to 4 decimal places. Round other answers to 3 decimal places.)

H0: β1 = 0 is	; Reject H0at α = (Click to select)0.050.0010.01
H0: β2 = 0 is	; Reject H0at α = (Click to select)0.0010.000010.00005
H0: β3 = 0 is	; Reject H0at α = (Click to select)0.0010.010.05

(5) Calculate the 95 percent confidence interval for β_j. (Round your answers to 3 decimal places.)

	95% C.I.
β0	[, ]
β1	[, ]
β2	[, ]
β3	[, ]

(6) Calculate the 99 percent confidence interval for β_j. (Round your answers to 3 decimal places.)

	95% C.I.
β0	[, ]
β1	[, ]
β2	[, ]
β3	[, ]

Answer 1

ANSWER:

Given that,

1)

	bj	sbj	t
H0: β0 = 0	1946.8020	504.1819	0.0023
H0: β1 = 0	0.0386	0.0130	0.0120
H0: β2 = 0;	1.0394	0.0676	2.91E-09
H0: β3 = 0	-413.7578	98.5983	-4.1964

2)

Using the t statistic and appropriate critical values, test H0: βj = 0 versus Ha: βj ≠ 0 by setting αequal to .05. Which independent variables are significantly related to y in the model with α =.05

	t critical	Decision
H0: β0 = 0	2.179	REJECT H0
H0: β0 = 0	2.179	REJECT H0
H0: β0 = 0	2.179	REJECT H0
H0: β0 = 0	2.179	REJECT H0

3)

Using the t statistic and appropriate critical values, test H0: βj = 0 versus Ha: βj ≠ 0 by setting αequal to .01. Which independent variables are significantly related to y in the model with α = .01

	t critical	Decision
H0: β0 = 0	3.054	REJECT H0
H0: β1 = 0	3.054	FAIL TO REJECT H0
H0: β2 = 0	3.054	REJECT H0
H0: β3= 0	3.054	REJECT H0

4)

H0: β1 = 0: REJECT H0 AT 0.05

H0: β2 = 0 ; REJECT H0 AT 0.000005

H0: β3 = 0; REJECT H0 0.05

	95% C.I
β0	[848.284,3045.320]
β1	[0.010,0.067]
β2	[0.892,1.187]
β2	[-628.585,-198.931]

5)

	bj	sbj	Lower 95%	Upper 95%
β0	1946.802	504.1819	848.284	3045.32
β1	0.0386	0.013	0.0102	0.067
β2	1.0394	0.0676	0.8922	1.1866
β3	-413.7578	98.5983	-628.585	-198.931

6)

bj	sbj	Lower 99%	Upper 99%
1946.802	504.1819	406.758428	3486.846
0.0386	0.013	-0.00110901	0.078309
1.0394	0.0676	0.83291312	1.245887
-413.7578	98.5983	-714.93021	-112.585