15. What is the estimate of the standard deviation of , the model error term? Ro
ID: 3314563 • Letter: 1
Question
15. What is the estimate of the standard deviation of , the model error term? Round your answer to four decimal places.
16. Compute the lower limit of a 95% confidence interval for 1, the model slope. Round your answer to four decimal places.
17. Compute the upper limit of a 95% confidence interval for 1, the model slope. Round your answer to four decimal places.
18. Compute the Student’s t test statistic for testing the null hypothesis H0 : 1 = 0.
19. Determine the critical value for the above statistical test using = 0.01.
20. The data provide sufficient evidence, at the 0.01 level of statistical significance, to conclude that the true slope differs from zero. True or False?
21. Predict the COA for a brick with a pore volume of 1.5 cm3/g.
22. Compute r2, the coefficient of determination.
23. Compute the correlation coefficient.
Questions 13-23: The coefficient of absorption (COA) for a clay brick is the ratio of the amount of cold water to the amount of boiling water that the brick will absorb. The output below from JMP shous a regression analysis predicting COA from the pore volume (in cm/g) of 7 bricks. Some portions of the output have been omitted. Ex 7.3.7- Fit Y by X of COA by PoreVol Bivariate Fit of COA By PoreVol 0.8 0.75 0.7 0.65 1.3 1.4 1.5 1.6 1.7 1.8 PoreVol Linear Fit Linear Fit Summary of Fit RSquare RSquare Adj Root Mean Square Error Mean of Response Observations (or Sum Wgts) 0.728571 7 Analysis of Variance Sum of DF Source Model Error C. Total Squares Mean Square F Ratio 1 0.02228026 0.00240545 0.022280 Parameter Estimates Term Intercept0.114532 0.09061 Estimate Std Error t Ratio Prob> PoreVol 0.3968494 0.058315 13. What is the value of o, the estimated intercept? Round your answer to four decimal places. 14. What is the value of B1, the estimated slope Round your answer to four decimal places 3 15. what is the estimate of the standard deviation of , the model error term? Round your answer to four decimal places.Explanation / Answer
Result:
13). 0.1145
14). 0.3968
15). Standard deviation =sqrt(0.00240545/5) =0.0219
16. Compute the lower limit of a 95% confidence interval for 1, the model slope. Round your answer to four decimal places.
Lower limit = 0.3968494-2.571*0.058315
=0.2469
17. Compute the upper limit of a 95% confidence interval for 1, the model slope. Round your answer to four decimal places.
upper limit = 0.3968494+2.571*0.058315
=0.5468
18. Compute the Student’s t test statistic for testing the null hypothesis H0 : 1 = 0.
t =0.3968494/0.058315 = 6.80527
19. Determine the critical value for the above statistical test using = 0.01.
Critical t=4.032
20. The data provide sufficient evidence, at the 0.01 level of statistical significance, to conclude that the true slope differs from zero. True or False?
True
21. Predict the COA for a brick with a pore volume of 1.5 cm3/g.
Predicted COA = 0.114532+0.3968494*1.5
=0.70981
22. Compute r2, the coefficient of determination.
R square =0.02228026/(0.02228026+0.00240545)
=0.90256
23. Compute the correlation coefficient.
Correlation r= sqrt(0.90256)
=0.950032
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