Construct a 90% prediction interval for a single value of y for the following da

Question

Construct a 90% prediction interval for a single value of y for the following data; use x = 100. Construct a 90% prediction interval for a single value of y for the following data; use x = 130. Compare the results. Which prediction interval is greater? Why?

(Do not round the intermediate values. Round your answers to 3 decimal places.)


90% prediction interval for a single value of y with x = 100: ______   y _____   

90% prediction interval for a single value of y with x = 130: ________ y ______

x y 140 25 119 29 103 44 91 70 67 88 29 111 24 128

Explanation / Answer

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: y
Independent Variable: x
y = 144.32751 - 0.89928895 x
Sample size: 7
R (correlation coefficient) = -0.98326468
R-sq = 0.96680943
Estimate of error standard deviation: 8.043913

Parameter estimates:

Analysis of variance table for regression model:

Predicted values:

Predicted values:

Hence,

90% prediction interval for a single value of y with x = 100: 36.858 < y < 71.939

90% prediction interval for a single value of y with x = 130: 8.645 < y < 46.195

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 144.32751 6.815403 0 5 21.176666 <0.0001 Slope -0.89928895 0.074516278 0 5 -12.068356 <0.0001

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