In an effort to explain the maximum yield in a chemical reaction, the following independent/predictor variables...

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In an effort to explain the maximum yield in a chemical reaction, the following independent/predictor variables were predetermined by the experimenter: temperature (°C) was the first predictor (x₁), the concentration of the reagent (%) was the second predictor (x₂) and third and final predictor (x₂) was the reaction of time (hours). The response variable (y) was the percentage of unchanged material. Table 2 below presents the dataset for the chemical reaction data. Table 2: Chemical Reaction data 41.5 33.7 27.7 21.7 10.0 15.0 12.2 4.3 10.3 6.4 37.6 18.0 26.3 9.9 25.0 14.1 15.2 15.9 y 19.6 162 162 152 162 172 172 172 172 167 177 157 167 167 167 167 x₁ 177 177 160 160 23 23 30 30 25 25 30 30 27.5 27.5 27.5 32.5 22.5 27.5 27.5 20 20 34 34 15. 8 5 8 5 B 6.5 6.5 6.5 6.5 6.5 9.5 35 6.5 6.5 17.6 7.5 2.1 Define what a design matrix is and give the design matrix for the chemical reaction data. (5) (4) 2.2 List and explain four assumptions underlying a multiple linear regression model. 2.3 In the case where the data does not satisfy all or some assumptions listed in part 2.2, what should a statistician do? (1) 2.4 Give the fitted equation of the multiple linear regression model Y₁ = Bo + B1x1 + B₂x2 + B3x3 + ₁ for the chemical reaction data. Interpret the coefficients. (15) In an effort to explain the maximum yield in a chemical reaction, the following independent/predictor variables were predetermined by the experimenter: temperature (°C) was the first predictor (x₁), the concentration of the reagent (%) was the second predictor (x₂) and third and final predictor (x₂) was the reaction of time (hours). The response variable (y) was the percentage of unchanged material. Table 2 below presents the dataset for the chemical reaction data. Table 2: Chemical Reaction data 41.5 33.7 27.7 21.7 10.0 15.0 12.2 4.3 10.3 6.4 37.6 18.0 26.3 9.9 25.0 14.1 15.2 15.9 y 19.6 162 162 152 162 172 172 172 172 167 177 157 167 167 167 167 x₁ 177 177 160 160 23 23 30 30 25 25 30 30 27.5 27.5 27.5 32.5 22.5 27.5 27.5 20 20 34 34 15. 8 5 8 5 B 6.5 6.5 6.5 6.5 6.5 9.5 35 6.5 6.5 17.6 7.5 2.1 Define what a design matrix is and give the design matrix for the chemical reaction data. (5) (4) 2.2 List and explain four assumptions underlying a multiple linear regression model. 2.3 In the case where the data does not satisfy all or some assumptions listed in part 2.2, what should a statistician do? (1) 2.4 Give the fitted equation of the multiple linear regression model Y₁ = Bo + B1x1 + B₂x2 + B3x3 + ₁ for the chemical reaction data. Interpret the coefficients. (15)

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1A design matrix is a matrix that shows the independent variables or predictors in a regression model It is sometimes referred to as an X matrix or predictor matrix To make the analysis easier the val... View the full answer