Location sales (in thousands) advertising (in thousands) adv^2 years in business adv*years dwest dsouthsouth 340 8 4 north 651 42 6 west 459 35 2 west 1400 65 16 north 943 40 11 south 425 24 4 west 589 10 8 south 492 17 7 north 490 15 8 south 920 33 15 north 1040 45 14 west 403 30 3 south 594 27 8 south 599 30 10 west 293 12 4 north 855 40 12 south 343 19 6 west 891 45 12 north 395 20 3 west 862 40 12 south 350 12 5 west 871 48 11 north 405 22 2 south 193 8 3 south 185 10 2
assignment: we are trying to explain the variation in sales from storefront to storefront using advertising budgets, years in business, and store location. ad^2 is a quadratic term for advertising. adv*years in an interaction term. for store location, north will be the omitted category or null state, and dsouth and dwest are dummy variables for stores located in the south or west.1. complete the data for adv^2, adv*years, south, and west. regress sales on advertising, adv^2, years in business, adv*years, south, and west.2. predict sales for a store in the west with $30,000 in advertising expenditures and 5 years in business.3. rank the regions based on sales from highest to lowest, holding adv and years in business constant.

1 and 2

step-by-step explanation:

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:

answer: 0.64

step-by-step explanation: