Question

An experiment is conducted to understand how the yield of a bacteria culture is affected by the amount of an additive (g) and temperature (C). The following multiple quadratic regression model was developed where x1 indicates the additive amount and x2 indicates the temperature REGRESSION MODEL Y1+ x1+ x2+ x1*x2 x1 2 x22 ESTIMATED COEFFICIENTS: ESTIMATIE SE TSTAT PVALUE ( INTERCEPT ) xl x2 x1: x2 x142 x2 2 -1194.7 414.99 9.5278 -1.0003 -46.042 -0.021687 194.48 51.696 2.2312 0.1867 7.7794 0.0070014 -3.0976 0.011297 -6.1432 0.00010929 8.0274 4.2702 5.3578 0.00032001 -5.9184 0.00014735 1.1427E-05 0.0016365 Using all the terms of the regression model given above, estimate the bacteria yield when the amount of additive is 2.3 g and the temperature is 140 °C.. a) 201.3145 b) There is not enough data to estimate the bacteria yield c) 102.9450 d) 817.2489 e) 1135.168

An experiment is conducted to understand how the yield of a bacteria culture is affected by the amount of an additive (g) and temperature ( oC). The following multiple quadratic regression model was developed where x1 indicates the additive amount and x2 indicates the temperature. REGRESSION MODEL: Y ~ 1 + X1+ X2+ X1*X2 + X1^2 + X2^2 ESTIMATED COEFFICIENTS: ESTIMATE SE TSTAT PVALUE _________ _________ _______ __________ (INTERCEPT) -1194.7 194.48 -6.1432 0.00010929 X1 414.99 51.696 8.0274 1.1427E-05 X2 9.5278 2.2312 4.2702 0.0016365 X1:X2 -1.0003 0.1867 -5.3578 0.00032001 X1^2 -46.042 7.7794 -5.9184 0.00014735 X2^2 -0.021687 0.0070014 -3.0976 0.011297 Using all the terms of the regression model given above, estimate the bacteria yield when the amount of additive is 2.3 g and the temperature is 140 oC.. a) 201.3145 b) There is not enough data to estimate the bacteria yield c) 102.9450 d) 817.2489 e) 1135.168

Answer 1

Regression model:

From above given output, regression equation is:

x1= additive=2.3

x2=temperature= 140

Answer: C