Describe each of the following vocabulary terms. for each, explain what they look like on a graph, why we'd care about them, and how they would affect our decision to model.
a) horizontal
b) trend
c) cycle / seasonal

a) Horizontal: When the scatter plot of a data set presents a graph that oscillates around a constant value with respect to the response variable. Suggest that the model is stationary on mean.

b) Trend: The data has a tendency when the scatter plot presents a behavior that approximates a relationship that can be, linear, quadratic, etc. The trend suggests that the model is not stationary on mean and this must be corrected before the estimation process.

c) Cycle / Seasonal: The cycle refers to the repetitive, periodic behavior of the data with respect to approximately equal time spaces. The cycle refers to extra annual periods and seasonality to intra annual periods. Seasonality and the cycle suggest that the model is not stationary on mean and this must be corrected before the estimation process.

Step-by-step explanation:

the revenue of the fitness center, y, is the product of two factors: the number of members and the fee paid by each member. there are 320 members now, but number of members goes down by 10 for each $5 increase in fees, so if x is the number of $5 price increases then members is equal to (320 - 10x). since the fee is currently $45, and the fee increases by $5 for every price bump x, the fee is given by (45 + 5x). so, revenue y is given by y = (320 - 10x)(45 + 5x).