The tensile strength of a paper product is related to the amount of hardwood in
ID: 3207561 • Letter: T
Question
The tensile strength of a paper product is related to the amount of hardwood in the pulp. Ten samples are produced in the pilot plant, and the data obtained are shown in the following table. a. Fit a linear regression model relating the strength to percent hardwood (x). Test the model in part (a) for significance of regression at alpha = 0.05. Find a 95% confidence interval on the parameter beta_1. Find a 95% confidence interval on the parameter beta_0. Find a 95% confidence interval on the mean response (y) when x = 28. Find a 95% prediction interval on the mean of four future observations when x = 28.Explanation / Answer
Result:
Regression Analysis
r²
0.970
n
10
r
0.985
k
1
Std. Error
2.203
Dep. Var.
strength
ANOVA table
Source
SS
df
MS
F
p-value
Regression
1,262.0672
1
1,262.0672
260.00
2.20E-07
Residual
38.8328
8
4.8541
Total
1,300.9000
9
Regression output
confidence interval
variables
coefficients
std. error
t (df=8)
p-value
95% lower
95% upper
Intercept
143.8244
2.5215
57.039
9.91E-12
138.0097
149.6390
Percent Hardwood
1.8786
0.1165
16.125
2.20E-07
1.6100
2.1473
Predicted values for: strength
95% Confidence Interval
95% Prediction Interval
Percent Hardwood
Predicted
lower
upper
lower
upper
Leverage
28
196.426
193.912
198.941
190.757
202.095
0.245
The regression line
Strength = 143.8244+1.8786*Percent Hardwood
Calculated F=260.0, P=0.000 which is < 0.05 level.
The model is significant.
95% CI for b1 is (1.6100, 2.1473)
95% CI for b0 is (138.0097, 149.6390)
95% CI for y when x=28 is (193.912, 198.941)
95% PI for y when x=28 is (190.757, 202.095)
Regression Analysis
r²
0.970
n
10
r
0.985
k
1
Std. Error
2.203
Dep. Var.
strength
ANOVA table
Source
SS
df
MS
F
p-value
Regression
1,262.0672
1
1,262.0672
260.00
2.20E-07
Residual
38.8328
8
4.8541
Total
1,300.9000
9
Regression output
confidence interval
variables
coefficients
std. error
t (df=8)
p-value
95% lower
95% upper
Intercept
143.8244
2.5215
57.039
9.91E-12
138.0097
149.6390
Percent Hardwood
1.8786
0.1165
16.125
2.20E-07
1.6100
2.1473
Predicted values for: strength
95% Confidence Interval
95% Prediction Interval
Percent Hardwood
Predicted
lower
upper
lower
upper
Leverage
28
196.426
193.912
198.941
190.757
202.095
0.245
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