Conceptual: In a dataset the response variable is mpg obtained in highway driving for midsized cars. A fuel additive is used to boost the mileage. Amount of additive used (X1) is an explnatory variable. Different types of fuels (octane types 89, 91 and 93) are used. It is assumed that the octane type interacts with the fuel additive in theor effect on mpg.

2. Conceptual: In a dataset the response variable is mpg obtained in highway driving for midsized cars. A fuel additive is used to boost the mileage. Amount of additive used (X1) is an explnatory variable. Different types of fuels (octane types 89, 91 and 93) are used. It is assumed that the octane type interacts with the fuel additive in theor effect on mpg. a) Define appropriate number of Indicator variables to replace the qualitative variable. b) Propose a model where fuel type interacts with the amount of additive used. c) Express the equations and Plot the mean response functions for different fule type. d) Interpret the parameters Bo, B1, 32 and one of the interaction coefficients. e) Suppose you want to test the hypothesis that there is no effect of fuel type. What is your Ho? f) Suppose you want to test the hypothsis that effect of additive on mpg is same for octane 91 and octane 93. What will be your Ho