Question

In: Statistics and Probability

Consider the set of ordered pairs shown below. Assuming that the regression equation is y= 5.594...

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.)

Solutions

Expert Solution

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


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