Chap 10 Exercises

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Exercise 3 The model \[\hspace{-2in}\text{price}(\text{livingArea}, \text{bedrooms}, \text{bathrooms}) \equiv\\\] \[ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 21000 + 105\,\text{livingArea} - 13000\, \text{bedrooms} + 26000\, \text{bathrooms}\] is described in the text as being a linear combination of functions. Which of these best describe those functions?

There are no functions, just inputs.

Three identity functions, each of which takes a different input.

Four identity functions, each of which takes a different input.

Three identity functions, each of which takes a different input, and a fourth function, namely the constant function \(\text{const}(x) \equiv 1\)

question id: identity-constant

Exercise 4 Even if you don’t yet have a theoretical understanding of how to construct functions with multiple inputs from data, you can R/mosaic operations for doing so. A key function is fitModel(), which like makeFun(), constructs a function. And, like makeFun(), you need to use a tilde expression to specify the model formula. But, unlike makeFun(), you can leave it to the computer to find the parameters that will make the function align with data.

To illustrate, we can construct a housing-price model from the SaratogaHouses data:

Note that in applying the price() function to inputs, we are using the names of the inputs explicitly. To write the command price(2000,3,2) risks mixing up which input is which.

Use the function in the ordinary way. For instance, here is what the model has to say about the anticipated sales price of a house with 2000 square feet of living area, three bedrooms, and two bathrooms.

For technical reasons, the functions created by fitModel() have a lot of computer-programming jargon in them, as you can see by constructing the model itself and then looking at the function. But you will also see the values of the parameters found by fitModel().

Class activity