Question

A statistical program is recommended.

Consider the following data for a dependent variable y and two independent variables,

x₁

and

x₂.

x1	x2	y
30	12	94
47	10	108
25	17	112
51	16	178
40	5	94
51	19	175
74	7	170
36	12	117
59	13	142
76	16	211

The estimated regression equation for the data is

ŷ = −18.4 + 2.01x₁ + 4.74x₂.

(a)

Develop a 95% confidence interval for the mean value of y when

x₁ = 74 and x₂ = 7.

(Round your answers to three decimal places.)

_____ to_____

(b)

Develop a 95% prediction interval for y when

x₁ = 74 and x₂ = 7.

(Round your answers to three decimal places.)

______ to ______

Answer 1

applying multiple regression from megastat: with x1=74 and x2=7 :

below is output":

Regression output					confidence interval
variables	coefficients	std. error	t (df=7)	p-value	95% lower	95% upper
Intercept	-18.3683	17.9715	-1.022	.3408	-60.8641	24.1276
x1	2.0102	0.2471	8.134	.0001	1.4258	2.5945
x2	4.7378	0.9484	4.995	.0016	2.4951	6.9805
Predicted values for: y
			95% Confidence Interval		95% Prediction Interval
x1	x2	Predicted	lower	upper	lower	upper
74	7	163.550	142.369	184.731	126.783	200.317

a)

95% confidence interval for the mean value of y =142.369 to 184.731

b)

95% prediction interval for y =126.783 to 200.317