In study, we used on pull strength of a wire bond in a semi - model. These displays can be helpful in visualizing the relationship among variables in a multivariable data set. Pull Strength Wire length |Die Height Pull Strength Wire Length Die Height 9.95 2 50 11.66 2 360 24.45 8 110 21.65 4 205 31.75 11 12 17.89 4 400 35.00 10 550 69.00 20 600 25.02 8 295 10.30 1 585 16.86 4 200 34.93 10 540 14.38 2 375 46.59 15 250 9.60 2 52 44.88 15 290 24.35 9 100 54.12 16 510 27.50 8 300 56.63 17 590 17.08 4 412 22.13 6 100 37.00 11 400 21.15 5 400 41.95 12 500 Estimated Multiple Regression " = bo + b1x1 + b2x12+ .".+ bnxin bo the intercept = use 6 decimal places) b, = wire length = (use 6 decimal places) b2 = die height = (use 6 decimal places) Multiple regression equation for Pull Strength D = bo + b1x11 + b2x12 pull strength = X1 X2 pull strength = 2 deicmal places + 2 decimals places x1 + 2 decimals places x2 multiple regression equation What is the predicted pull strength? (Complete the table) D = bo + b1X11 + b2x12 Pull predicted Wire Die pull Strength length Height strength 9.95 2 50 2 : decimal ... places 21.15 5 400 Hypothesis Test of Significance for the individual parameters: 1. Is there significant effect between pull strength and wire length? Ho: Bi = 0 (State your statement) Ha: Bi # 0 (State your statement)Test Statistics: t = = _ (2 decimal places) Rejection Rule: Reject Ho ifp - value S a Or if tcomputed S -ta (t - table) based on t distribution table Or if tcomputed 2 ta (t - table) based on t distribution table a = 0.05 , " = 0.025 Degree of freedom: n - p - 1 Where n is the sample size. n = p is the number of independent variables or number of x terms p = df =. https://www.sisu.edu/faculty/gerstman/StatPrimer/t-table.pdf Rejection Rule: if |tcomputed value| > ttable Reject the null hypothesis, accept the alternative hypothesis Decision: Conclusion: 2. Is there significant effect between pull strength and die height? Ho: Bi = 0 (State your statement) Ha: Bi # 0 (State your statement) Test Statistics: t = (2 decimal places) Rejection Rule: Reject Ho if p - value S a Or if tcomputed S -ta (t - table) based on t distribution table Or if tcomputed 2 ta (t - table) based on t distribution table a = 0.05 , " = 0.025 Degree of freedom: n - p - 1 Where n is the sample size. n = p is the number of independent variables or number of x terms p = df = https://www.sisu.edu/faculty/gerstman/StatPrimer/t-table.pdf > Rejection Rule: if |tcomputed value| > ttable Reject the null hypothesis, accept the alternative hypothesis Decision: Reject Ho and accept Ha Conclusion: there is NO significant effect between pull strength and die height Now let's proceed the overall significance F (p - value) > Hypothesis: Ho: B1 = B2 = B3 = 0 (State your statement) Ha: Bi # 0 (State your statement) If p - value > a, fail to reject the Null hypothesis Decision:Conclusion: Another method: F - stat > p - value , Reject the null hypothesis ad accept alternative hypothesis F - stat > p - value Decision: Conclusion