Question

The regression equation for the given paired data is y-73012+ 0.8859x and the standard error of estimate is se-278807. Find the 95% prediction interval of y for x 37. Round to the nearest tenth x25 26 36 36 40 48 ?! 95 95 102 109 110 114 ? A. 73,0 < y < 114.2 ??. 97.4cyc 114.2 ° C. 73.0 < y < 105.8 O D. 97.4< y< 10.8

x y

25 95

26 95

36 102

36 109

40 110

48 114

0 0
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Answer #1

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: y
Independent Variable: x
y = 73.012826 + 0.8858912 x
Sample size: 6
R (correlation coefficient) = 0.95124387
R-sq = 0.9048649
Estimate of error standard deviation: 2.7880693

Parameter estimates:

Parameter Estimate Std. Err. Alternative DF T-Stat P-value
Intercept 73.012826 5.1774635 ? 0 4 14.102045 0.0001
Slope 0.8858912 0.14362462 ? 0 4 6.168101 0.0035


Analysis of variance table for regression model:

Source DF SS MS F-stat P-value
Model 1 295.74001 295.74001 38.04547 0.0035
Error 4 31.093322 7.7733304
Total 5 326.83333


Predicted values:

X value Pred. Y s.e.(Pred. y) 95% C.I. for mean 95% P.I. for new
37 105.7908 1.1682843 (102.54712, 109.03448) (97.39775, 114.18385)

Hence,

95% prediction interval will be:

97.4 < y < 114.2

Option B is correct.

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