Question

Consider the set of ordered pairs shown below. Assuming that the regression equation is y= 5.594 minus 0.189 x and the SSE equals 6.27​, construct a​ 95% confidence interval for xequals4.    x 2 7 3 4 5    y 6 5 4 6 3 LOADING... Calculate the upper and lower limits of the confidence interval. UCL equals nothing LCL equals nothing ​(Round to three decimal places as​ needed.)

Answer 1

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: y
Independent Variable: x
y = 5.5945946 - 0.18918919 x
Sample size: 5
R (correlation coefficient) = -0.27910828
R-sq = 0.077901431
Estimate of error standard deviation: 1.4457144

Parameter estimates:

Parameter	Estimate	Std. Err.	Alternative	DF	T-Stat	P-value
Intercept	5.5945946	1.7056317	≠ 0	3	3.2800719	0.0464
Slope	-0.18918919	0.37579556	≠ 0	3	-0.50343647	0.6493

Analysis of variance table for regression model:

Source	DF	SS	MS	F-stat	P-value
Model	1	0.52972973	0.52972973	0.25344828	0.6493
Error	3	6.2702703	2.0900901
Total	4	6.8

Predicted values:

X value	Pred. Y	s.e.(Pred. y)	95% C.I. for mean	95% P.I. for new
4	4.8378378	0.650897	(2.7663931, 6.9092826)	(-0.20787734, 9.883553)

Hence,

95% confidence interval for x = 4 will be:

UCL = 6.909

LCL = 2.766