Q1: Many companies manufacture products that are at least partially produced using chemicals (e.g., paint, gasoline,...

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Q1: Many companies manufacture products that are at least partially produced using chemicals (e.g., paint, gasoline, and stell). In many cases, the quality of the finished product is a function of the tempreture and pressure at which the chemical reasctions take place, and whether the raw material is from one of the certain brands. Suppose that a particular manufacturer wants to model the quality (y) of a product as a function of the templrature (X1), the pressure (X2) at which it is produced, and its brand. The data in the "Data" sheet in this document contains data obtained from a carefully designed experiment involving these variables. Note that the assigned quality score can range from a minimum of 0 to a maximum of 100 for each manufactured product. The categorical variable equals to "Yes" if the raw material of the product is from certain brands. Note that categorical variables need to be transformed into numeric form before running them in a regression. a) Estimate a multiple regression equation that includes the three given explanatory variables. Report your regression results in a new sheet in this document. Does the estimated equation fit the data well? b) Write down the null hypothesis to test statistical significance of the coefficient estimates; a seperate null hypothesis for each coefficient. Based on the regression outputs, do you reject or fail to reject the null hypotheses? What does that mean? Interpret your results for each coefficient and variable. c) Create an interruction term between tempreture and pressure (create a new data column that multiplies Temperature with Pressure. You can use this formula: =Temperature*Pressure. Run the regression again now with three explanatory variables; "Temperature," "Pressure", and "Temperature *Pressure." Does the inclusion of interruction term improve the model's goodness of fit? d) For this new model, write down the null hypothesis to test statistical significance of the coefficient estimates; a seperate null hypothesis for each coefficient. Based on the regression outputs of this second model, do you reject or fail to reject the null hypotheses? What does that mean? Interpret your results for each coefficient and variable. e) How are your regression outputs of the second model different from the regressio outputs of the first model? Q1: Many companies manufacture products that are at least partially produced using chemicals (e.g., paint, gasoline, and stell). In many cases, the quality of the finished product is a function of the tempreture and pressure at which the chemical reasctions take place, and whether the raw material is from one of the certain brands. Suppose that a particular manufacturer wants to model the quality (y) of a product as a function of the templrature (X1), the pressure (X2) at which it is produced, and its brand. The data in the "Data" sheet in this document contains data obtained from a carefully designed experiment involving these variables. Note that the assigned quality score can range from a minimum of 0 to a maximum of 100 for each manufactured product. The categorical variable equals to "Yes" if the raw material of the product is from certain brands. Note that categorical variables need to be transformed into numeric form before running them in a regression. a) Estimate a multiple regression equation that includes the three given explanatory variables. Report your regression results in a new sheet in this document. Does the estimated equation fit the data well? b) Write down the null hypothesis to test statistical significance of the coefficient estimates; a seperate null hypothesis for each coefficient. Based on the regression outputs, do you reject or fail to reject the null hypotheses? What does that mean? Interpret your results for each coefficient and variable. c) Create an interruction term between tempreture and pressure (create a new data column that multiplies Temperature with Pressure. You can use this formula: =Temperature*Pressure. Run the regression again now with three explanatory variables; "Temperature," "Pressure", and "Temperature *Pressure." Does the inclusion of interruction term improve the model's goodness of fit? d) For this new model, write down the null hypothesis to test statistical significance of the coefficient estimates; a seperate null hypothesis for each coefficient. Based on the regression outputs of this second model, do you reject or fail to reject the null hypotheses? What does that mean? Interpret your results for each coefficient and variable. e) How are your regression outputs of the second model different from the regressio outputs of the first model?