# Statistics - Linear Trend - Regression

1. Give one example of each of the following:

A) Trend Component. Explain why it is a trend component.

B) Seasonal Component. Explain why it is a seasonal component.

C) Cyclical Component. Explain why it is a cyclical component.

D) Irregular (Random) Component. Explain why it is an irregular component.

2. Give three real life examples of each of the following:

A) Linear trend. Explain why it is a linear trend.

B) Non-linear trend. Explain why it is a non-linear trend.

3. Mr. Samuelson is a car sales associate. He makes a salary of $600 per week. He also earns a bonus of $200 for each car he sells. Write a simple linear regression equation that represents the total amount of money (y) Mr. Samuelson earns in a week when he sells Â¿xÂ¿ number of cars.

[Please see the attached question file].

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#### Solution Preview

1. (A) Trend (Secular trend) Component

The term "trend" is commonly used in day-to-day conversation. We often complain about the rising trend of population, prices etc. "Trend", also called "Secular" or "long-term" trend is the basic tendency of production, sales, income, employment etc. to grow or decline over a period of time. It includes steady movements over a long time and excludes short-range oscillations.

Secular trend is attributable to factors such as population change, technological progress or large-scale shifts in consumer tastes. More populations call for more food, more clothing and more housing. Technological changes, discovery or depletion of resources, improvements in business organization and Government intervention in the economy are other major causes for the growth or decline of many economic time series.

Secular trends may be linear or nonlinear.

(B) Seasonal Component

Seasonal variations are those periodic movements in business activity which occur regularly every year and have their origin in the nature of the year itself. Since they repeat over a period of 12 months, they can be predicted fairly accurately. Almost any type of business activity is susceptible to a seasonal influence to a greater or lesser degree and as such these variations are regarded as normal phenomena during every year. Although the word "seasonal" seems to connect with a season of the year, the term is meant to include any type of variation which is periodic in nature and whose repeating cycles are of a ...

#### Solution Summary

Neat, step-by-step solutions are provided explaining different components, as well as real-life examples of linear/non-linear trends are given. Please see attached file.