Develop a multiple linear regression model to predict the price of a house using the square feet of living area, number of bedrooms, and number of bathrooms as the predictor variables Write the reqression equation.
Discuss the statistical significance of the model as a whole using the appropriate regression statistic at a 95% level of confidence.
Discuss the statistical significance of the coefficient for each independent variable using the appropriate regression statistics at a 95% level of confidence.
Interpret the coefficient for each independent variable.
What percentage of the observed variation in housing prices is explained by the model?
Determine the prediction interval of a house with 3,000 square feet of living area, 3 bedrooms, and 2.5 bathrooms, and comment on the prediction interval.
Prepare a single Microsoft Excel file to document your regression analyses. Prepare a single Microsoft Word document that outlines your responses for each portion of the case study.

Selling Price Living Area (Sq Feet) No. Bathrooms No Bedrooms Age (Years)

$240,000 2,022 2.5 3 20

$235,000 1,578 2 3 20

$500,075 3,400 3 3 20

$240,000 1,744 2.5 3 20

$270,000 2,560 2.5 3 20

$225,000 1,398 2.5 3 20

$280,000 2,494 2.5 3 20

$225,000 2,208 2.5 4 20

$248,220 2,550 2.5 3 20

$275,000 1,812 2.5 2 20

$137,000 1,290 1 2 20

$150,000 1,172 2 2 20

$649,000 4,128 3.5 3 20

$195,000 1,816 2.5 3 97

$373,200 2,628 2.5 4 20

$169,450 1,254 2.5 3 20

$144,200 1,660 1.5 4 20

$189,900 1,850 1.5 3 20

$166,000 1,258 2 3 20

$160,000 1,219 2 3 20

$327,355 1,850 2.5 3 20

$247,000 2,103 2.5 3 20

$318,000 1,806 2.5 3 20

$341,000 1,674 1.5 2 17

$288,650 2,242 2.5 3 20

$157,000 1,408 1.5 3 20

$449,000 3,457 2.5 3 21

$142,000 1,728 1.5 3 21

$389,000 2,354 2.5 3 21

$476,000 2,246 2.5 3 21

$249,230 1,902 2.5 2 21

$139,900 1,178 1 3 21

$301,900 2,896 3.5 4 21

$425,000 2,457 3 3 41

$121,000 936 1 3 50

$150,000 934 1 2 21

$138,000 1,279 1 3 21

$199,900 1,888 2 3 26

$145,000 1,686 1.5 4 21

$465,000 2,310 3 2 21

$158,000 1,200 1.5 3 21

when functions are first introduced, you will probably have some simplistic "functions" and relations to deal with, usually being just sets of points. these won't be terribly useful or interesting functions and relations, but your text wants you to get the idea of what the domain and range of a function are. small sets of points are generally the simplest sorts of relations, so your book starts with those.

step-by-step explanation:

state the domain and range of the following relation. is the relation a function?

{(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)}

the above list of points, being a relationship between certain x's and certain y's, is a relation. the domain is all the x-values, and the range is all the y-values. to give the domain and the range, i just list the values without duplication:

domain: {2, 3, 4, 6}

range: {–3, –1, 3, 6}

(it is customary to list these values in numerical order, but it is not required. sets are called "unordered lists", so you can list the numbers in any order you feel like. just don't duplicate: technically, repetitions are okay in sets, but most instructors would count off for this.)

while the given set does indeed represent a relation (because x's and y's are being related to each other), the set they gave me contains two points with the same x-value: (2, –3) and (2, 3). since x = 2 gives me two possible destinations (that is, two possible y-values), then this relation is not a function.

note that all i had to do to check whether the relation was a function was to look for duplicate x-values. if you find any duplicate x-values, then the different y-values mean that you do not have a function. remember: for a relation to be a function, each x-value has to go to one, and only one, y-value.

state the domain and range of the following relation. is the relation a function?

{(–3, 5), (–2, 5), (–1, 5), (0, 5), (1, 5), (2, 5)}

i'll just list the x-values for the domain and the y-values for the range:

i think it's eleven too, don't woosh me here, but according to the "experts" it's 2.

the proof starts from the peano postulates, which define the natural

numbers n. n is the smallest set satisfying these postulates:

  p1.   1 is in n.

  p2.   if x is in n, then its "successor" x' is in n.

  p3.   there is no x such that x' = 1.

  p4.   if x isn't 1, then there is a y in n such that y' = x.

  p5.   if s is a subset of n, 1 is in s, and the implication

      (x in s => x' in s) holds, then s = n.

then you have to define addition recursively:

  def: let a and b be in n. if b = 1, then define a + b = a'

      (using p1 and p2). if b isn't 1, then let c' = b, with c in n

      (using p4), and define a + b = (a + c)'.

then you have to define 2:

  def:   2 = 1'

2 is in n by p1, p2, and the definition of 2.

theorem:   1 + 1 = 2

proof: use the first part of the definition of + with a = b = 1.

      then 1 + 1 = 1' = 2   q.e.d.

note: there is an alternate formulation of the peano postulates which

replaces 1 with 0 in p1, p3, p4, and p5. then you have to change the

definition of addition to this:

  def: let a and b be in n. if b = 0, then define a + b = a.

      if b isn't 0, then let c' = b, with c in n, and define

      a + b = (a + c)'.

you also have to define 1 = 0', and 2 = 1'. then the proof of the

theorem above is a little different:

proof: use the second part of the definition of + first:

      1 + 1 = (1 + 0)'

      now use the first part of the definition of + on the sum in

      parentheses:   1 + 1 = (1)' = 1' = 2   q.e.d.