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The article "Optimization of Surface Roughness in Drilling Using Vegetable-Based Cutting Oils Developed from Sunflower Oil"t gave the following data on x, - spindle speed (rpm), x, - feed rate (mm/rev), x, - drilling depth (mm), and y - surface roughness (um) when a semisynthetic cutting fluid was used.

The article "Optimization of Surface Roughness in Drilling Using Vegetable-Based Cutting Oils Developed from Sunflower Oil"t gave the following data on x, - spindle speed (rpm), x, - feed rate (mm/rev), x, - drilling depth (mm), and y - surface roughness (um) when a semisynthetic cutting fluid was used.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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(b) Here is Minitab output from fitting the model with just x, and x, as predictors (the cited article made no mention of this model). Predictor Сoef SE Coef P Constant 0.365 1.514 0.24 0.817 -0.006767 0.002055 -3.29 0.017 45.67 10.28 4.44 0.004 S = 0.503400 R-Sg = 83.6$ R-Sq (adj) = 78.18 Carry out a test of model utility using a = 0.05. State the appropriate hypotheses. O H: B, = B, = 0 H.: H: at least one among B, B, is not zero 1' O Ho: B, + 8, + 0 H: B = B2 = 0 O H: B, = B2 = 0 H: no B, - 0 O H: B, + 8, +0 по 6. +B, 1 H: at least one among B,. B, is zero Calculate the test statistic. (Round your answer to two decimal places.) f = What can be said about the P-value for the test? O P-value > 0.100 O 0.050 < P-value < 0.100 O 0.010 < P-value < 0.050 O 0.001 < P-value < 0.010 O P-value < 0.001 State the conclusion in the problem context. O Reject Ho. The model based on x, and x, is judged not useful. O Reject H. The model based on x, and x, is judged useful. O Fail to reject H. The model based on x, and x, is judged useful. O Fail to reject H. The model based on x, and x, is judged not useful. o' (c) Calculate a 95% CI for the population regression coefficient on x,. (Round your answers to five decimal places.) ((-0.01250 X 1-0.00103 Interpret the CI. O we estimate that when there is a 1 mm/rev increase in feed rate the mean surface roughness in um will change by this amount, while the "spindle speed" predictor remains fixed. O we estimate that when there is a 1 mm/rev increase in feed rate the mean spindle speed in rpm will change by this amount, while the "surface roughness" predictor remains fixed. O we estimate that when there is a 1 pm increase in surface roughness the mean spindle speed in rpm will change by this amount, while the "feed rate" predictor remains fixed. We estimate that when there is a 1 rpm increase in spindle speed the mean surface roughness in pm will change by this amount, while the "feed rate" predictor remains fixed. O we estimate that when there is a 1 rpm increase in spindle speed the mean feed rate in mm/rev will change by this amount, while the "surface roughness" predictor remains fixed. (d) The estimated standard deviation of the predicted Y when x, = 400 and x, = 0.125 is 0.180. Calculate a 95% CI for true average roughness under these circumstances. (Round your answers to two decimal places.) um
Transcribed Image Text:(b) Here is Minitab output from fitting the model with just x, and x, as predictors (the cited article made no mention of this model). Predictor Сoef SE Coef P Constant 0.365 1.514 0.24 0.817 -0.006767 0.002055 -3.29 0.017 45.67 10.28 4.44 0.004 S = 0.503400 R-Sg = 83.6$ R-Sq (adj) = 78.18 Carry out a test of model utility using a = 0.05. State the appropriate hypotheses. O H: B, = B, = 0 H.: H: at least one among B, B, is not zero 1' O Ho: B, + 8, + 0 H: B = B2 = 0 O H: B, = B2 = 0 H: no B, - 0 O H: B, + 8, +0 по 6. +B, 1 H: at least one among B,. B, is zero Calculate the test statistic. (Round your answer to two decimal places.) f = What can be said about the P-value for the test? O P-value > 0.100 O 0.050 < P-value < 0.100 O 0.010 < P-value < 0.050 O 0.001 < P-value < 0.010 O P-value < 0.001 State the conclusion in the problem context. O Reject Ho. The model based on x, and x, is judged not useful. O Reject H. The model based on x, and x, is judged useful. O Fail to reject H. The model based on x, and x, is judged useful. O Fail to reject H. The model based on x, and x, is judged not useful. o' (c) Calculate a 95% CI for the population regression coefficient on x,. (Round your answers to five decimal places.) ((-0.01250 X 1-0.00103 Interpret the CI. O we estimate that when there is a 1 mm/rev increase in feed rate the mean surface roughness in um will change by this amount, while the "spindle speed" predictor remains fixed. O we estimate that when there is a 1 mm/rev increase in feed rate the mean spindle speed in rpm will change by this amount, while the "surface roughness" predictor remains fixed. O we estimate that when there is a 1 pm increase in surface roughness the mean spindle speed in rpm will change by this amount, while the "feed rate" predictor remains fixed. We estimate that when there is a 1 rpm increase in spindle speed the mean surface roughness in pm will change by this amount, while the "feed rate" predictor remains fixed. O we estimate that when there is a 1 rpm increase in spindle speed the mean feed rate in mm/rev will change by this amount, while the "surface roughness" predictor remains fixed. (d) The estimated standard deviation of the predicted Y when x, = 400 and x, = 0.125 is 0.180. Calculate a 95% CI for true average roughness under these circumstances. (Round your answers to two decimal places.) um
The article "Optimization of Surface Roughness in Drilling Using Vegetable-Based Cutting Oils Developed from Sunflower Oil" t gave the following data on x, = spindle speed (rpm), x, = feed rate (mm/rev), x, = drilling depth (mm), and y = surface roughness (um) when a semisynthetic cutting fluid was used. X1 X2 X3 y e* 320 0.10 15 2.27 -1.32 320 0.12 20 4.14 1.08 320 0.14 25 4.69 0.26 420 0.10 20 1.92 -0.40 420 0.12 25 2.63 -0.79 420 0.14 15 4.34 0.99 520 0.10 25 2.03 1.64 520 0.12 15 2.34 0.03 520 0.14 20 2.67 -1.52
Transcribed Image Text:The article "Optimization of Surface Roughness in Drilling Using Vegetable-Based Cutting Oils Developed from Sunflower Oil" t gave the following data on x, = spindle speed (rpm), x, = feed rate (mm/rev), x, = drilling depth (mm), and y = surface roughness (um) when a semisynthetic cutting fluid was used. X1 X2 X3 y e* 320 0.10 15 2.27 -1.32 320 0.12 20 4.14 1.08 320 0.14 25 4.69 0.26 420 0.10 20 1.92 -0.40 420 0.12 25 2.63 -0.79 420 0.14 15 4.34 0.99 520 0.10 25 2.03 1.64 520 0.12 15 2.34 0.03 520 0.14 20 2.67 -1.52
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