Question

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 = 65 and x2 = 10. (Round your answers to three decimal places.) _______ to _______

(b) Develop a 95% prediction interval for y when x1 = 65 and x2 = 10. (Round your answers to three decimal places.) _______ to _______

Answer 1

Excel regression output is given below(Megastat)

Regression Analysis
	R²	0.926
	Adjusted R²	0.904	n	10
	R	0.962	k	2
	Std. Error	12.710	Dep. Var.	y
ANOVA table
Source	SS	df	MS	F	p-value
Regression	14,052.1550	2	7,026.0775	43.50	.0001
Residual	1,130.7450	7	161.5350
Total	15,182.9000	9
Regression output					confidence interval
variables	coefficients	std. error	t (df=7)	p-value	95% lower	95% upper
Intercept	-18.3683
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	Leverage
65	10	159.672	145.203	174.141	126.317	193.027	0.232

from the output

a)

95% Confidence Interval
lower	upper
145.203	174.141

b)

95% Prediction Interval
lower	upper
126.317	193.027