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length, and die height. Observation number Pull strength (Y) Wire length (X1) Die Height (X2) 1 9.95 2 50 2 24.45 8 110 3 31.75 11 120 4 35.00 10 550 5 25.02 8 295 6 16.86 4 200 7 14.38 2 375 8 9.60 2 52 9 24.35 9 100 10 27.50 8 300 a i) Fit a regression line using pull strength as Y and wire length as X. Use calculator to find the a and b to do so. ii) Find the coefficient of correlation in this regression model. Interpret its meaning. iii) Find the coefficient of determination in this regression model. Interpret its meaning. b) Now the researcher wanted to include one more variable, Die Height, in the regression model. Thus he obtained the following Excel output using both wire length and die height as independent variables: SUMMARY OUTPUT Regression Statistics Multiple R 0.994525658 0.989081284 R Square Adjusted R Square 1.043637866 Standard Error Observations 10 ANOVA F Significance F Regression Residual Total SS MS 2 690.65018 7 7.624259961 698.27444 9 P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Standard Error t Stat 4.544350574 0.774648328 Intercept Wire length (X1) Die Height (X2) 2.215835576 0.101913929 0.014685417 0.002211316 df Coefficients

length, and die height. Observation number Pull strength (Y) Wire length (X1) Die Height (X2) 1 9.95 2 50 2 24.45 8 110 3 31.75 11 120 4 35.00 10 550 5 25.02 8 295 6 16.86 4 200 7 14.38 2 375 8 9.60 2 52 9 24.35 9 100 10 27.50 8 300 a i) Fit a regression line using pull strength as Y and wire length as X. Use calculator to find the a and b to do so. ii) Find the coefficient of correlation in this regression model. Interpret its meaning. iii) Find the coefficient of determination in this regression model. Interpret its meaning. b) Now the researcher wanted to include one more variable, Die Height, in the regression model. Thus he obtained the following Excel output using both wire length and die height as independent variables: SUMMARY OUTPUT Regression Statistics Multiple R 0.994525658 0.989081284 R Square Adjusted R Square 1.043637866 Standard Error Observations 10 ANOVA F Significance F Regression Residual Total SS MS 2 690.65018 7 7.624259961 698.27444 9 P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Standard Error t Stat 4.544350574 0.774648328 Intercept Wire length (X1) Die Height (X2) 2.215835576 0.101913929 0.014685417 0.002211316 df Coefficients

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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The following data is the pull strength of a wire bond in a semiconductor manufacturing process, wire length, and die height. Observation number Pull strength (Y) Wire length (X1) Die Height (X2) 1 9.95 2 50 2 24.45 8 110 3 31.75 11 120 4 35.00 10 550 5 25.02 8 295 6 16.86 4 200 7 14.38 2 375 8 9.60 2 52 9 24.35 9 100 10 27.50 8 300 a i) Fit a regression line using pull strength as Y and wire length as X. Use calculator to find the a and b to do so. ii) Find the coefficient of correlation in this regression model. Interpret its meaning. iii) Find the coefficient of determination in this regression model. Interpret its meaning. b) Now the esearcher wanted to include one more variable, Die Height, in the regression model. Thus he obtained the following Excel output using both wire length and die height as independent variables: SUMMARY OUTPUT Regression Statistics Multiple R 0.994525658 0.989081284 R Square Adjusted R Square Standard Error Observations 1.043637866 10 ANOVA MS F Significance F 2 Regression Residual Total SS 690.65018 7.624259961 7 9 698.27444 P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept Wire length (X1) Standard Error t Stat 4.544350574 0.774648328 2.215835576 0.101913929 Die Height (X2) 0.014685417 0.002211316 df Coefficients
Transcribed Image Text:The following data is the pull strength of a wire bond in a semiconductor manufacturing process, wire length, and die height. Observation number Pull strength (Y) Wire length (X1) Die Height (X2) 1 9.95 2 50 2 24.45 8 110 3 31.75 11 120 4 35.00 10 550 5 25.02 8 295 6 16.86 4 200 7 14.38 2 375 8 9.60 2 52 9 24.35 9 100 10 27.50 8 300 a i) Fit a regression line using pull strength as Y and wire length as X. Use calculator to find the a and b to do so. ii) Find the coefficient of correlation in this regression model. Interpret its meaning. iii) Find the coefficient of determination in this regression model. Interpret its meaning. b) Now the esearcher wanted to include one more variable, Die Height, in the regression model. Thus he obtained the following Excel output using both wire length and die height as independent variables: SUMMARY OUTPUT Regression Statistics Multiple R 0.994525658 0.989081284 R Square Adjusted R Square Standard Error Observations 1.043637866 10 ANOVA MS F Significance F 2 Regression Residual Total SS 690.65018 7.624259961 7 9 698.27444 P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept Wire length (X1) Standard Error t Stat 4.544350574 0.774648328 2.215835576 0.101913929 Die Height (X2) 0.014685417 0.002211316 df Coefficients
i) From the Excel output, fit a regression model using wire length as X1 and die height as X2. ii) Interpret the coefficient of X1 and X2. iii) Calculate the adjusted R square for this regression model. iv) Test the overall significance of this regression model at a = 0.05 v) Test the significance of X1 (wire length) and X2 (die height) respectively in the regression model at a = 0.05 vi) Estimate the pull strength of a wire bond with wire length is 3 and die height is 250. c) Comparing regression model in (a) and (b), which regression model should be used by the researcher?
Transcribed Image Text:i) From the Excel output, fit a regression model using wire length as X1 and die height as X2. ii) Interpret the coefficient of X1 and X2. iii) Calculate the adjusted R square for this regression model. iv) Test the overall significance of this regression model at a = 0.05 v) Test the significance of X1 (wire length) and X2 (die height) respectively in the regression model at a = 0.05 vi) Estimate the pull strength of a wire bond with wire length is 3 and die height is 250. c) Comparing regression model in (a) and (b), which regression model should be used by the researcher?
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