A real estate builder wishes to determine how house size (House) is influenced by family income (Income X1), family size (Size X 2), and education of the head of household (School X 3). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below: Coefficients Standard Error t Stat P-value Intercept -1.6335 5.8078 -0.281 0.7798 Income 0.4485 0.1137 3.955 0.0003 Size 4 .2615 0.8062 5.286 0.0001 School -0.6517 0.4319 -1.509 0.1383 What is the predicted house size (in hundreds of square feet) for an individual earning an annual income of $40,000, having a family size of 4, and going to school a total of 13 years? A) 11.43 B) 15.15 C) 24.88 D) 53.87
Minimization
In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.
Maxima and Minima
The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.
Derivatives
A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.
Concavity
In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.
A real estate builder wishes to determine how house size (House) is influenced by family income
(Income X1), family size (Size X 2), and education of the head of household (School X 3). House size is measured in
hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly
selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
Coefficients Standard Error t Stat P-value
Intercept -1.6335 5.8078 -0.281 0.7798
Income 0.4485 0.1137 3.955 0.0003
Size 4 .2615 0.8062 5.286 0.0001
School -0.6517 0.4319 -1.509 0.1383
What is the predicted house size (in hundreds of square feet) for an individual earning an annual income
of $40,000, having a family size of 4, and going to school a total of 13 years?
A) 11.43 B) 15.15 C) 24.88 D) 53.87
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