Some websites provide you with the opportunity to estimate the cost of building a house from scratch given the planned house square footage, and an index quantifying how luxurious you want your house to be. This index ranges from 1 to 5, where 1 is for very basic style, 3 for average style, and 5 for most luxurious style. The cost is estimated specifically for you by looking at houses recently built in your area, collecting their square footage, style index, and building cost, fitting a linear function, and then returning the cost associated with your particular specifications. This problem walks you through how this works in practice. Here is a table containing recent houses built, their square footage, their style index, and their building costs House A B Sqft (in units of 1000sqft) 1.5 3.0 1.1 2.3 1.8 Index 2 4 5 3 1 Cost (in units of $100,000) 4.3 7.5 5.0 6.0 3.9 E Let x be the square footage of the house (in units of 1000 sqft), y be the style index, and c(x, y) be the cost of building a house (in units of $100,000) given its square footage and style index. We want to fit a linear function through this data, of the kind c(x, y) = ax + by (1) Question 1: We want to find the best fit through the data. Using what you learned in the "Appli- cations of quadratic functions page, derive the expression for the error E(a,b) between the data and the model. You should obtain (after rounding the coefficients for simplicity) the following multivariate quadratic function of a and b: E(a,b) = 21a + 5562 + 58ab 111a 1716 + 151 Clearly show the steps of the calculation made to obtain this quadratic. Some websites provide you with the opportunity to estimate the cost of building a house from scratch given the planned house square footage, and an index quantifying how luxurious you want your house to be. This index ranges from 1 to 5, where 1 is for very basic style, 3 for average style, and 5 for most luxurious style. The cost is estimated specifically for you by looking at houses recently built in your area, collecting their square footage, style index, and building cost, fitting a linear function, and then returning the cost associated with your particular specifications. This problem walks you through how this works in practice. Here is a table containing recent houses built, their square footage, their style index, and their building costs House A B Sqft (in units of 1000sqft) 1.5 3.0 1.1 2.3 1.8 Index 2 4 5 3 1 Cost (in units of $100,000) 4.3 7.5 5.0 6.0 3.9 E Let x be the square footage of the house (in units of 1000 sqft), y be the style index, and c(x, y) be the cost of building a house (in units of $100,000) given its square footage and style index. We want to fit a linear function through this data, of the kind c(x, y) = ax + by (1) Question 1: We want to find the best fit through the data. Using what you learned in the "Appli- cations of quadratic functions page, derive the expression for the error E(a,b) between the data and the model. You should obtain (after rounding the coefficients for simplicity) the following multivariate quadratic function of a and b: E(a,b) = 21a + 5562 + 58ab 111a 1716 + 151 Clearly show the steps of the calculation made to obtain this quadratic