Answer to Question #252575 in Statistics and Probability for rasha

Question

The dataset in the below table represents the 4-month profits (in million $) of real estate company that operates in Egypt over the period of time between 2014-2018. I II III 2014 15.6 20.4 29.4 2015 13.8 23.2 35 2016 17.8 19.4 30.6 2017 21.4 24.8 33.6 2018 18.4 27.2 34.2 Answer the following questions: 1. Find the seasonal indices for the company’s profits and comment on the results. 2. Find the deseasonalized values of company’s profits and compare it to the actual values graphically. Comment on the results. 3. By using the deseasonalized values obtained in (2), determine the simple linear trend equation. And comment on the results. 4. Predict the expected value of company’s profit in summer 2019 which includes the effects of all the components of time series. And comment on the results.

Answer 1

1.

to find the seasonal indices we divide each quarterly profits figure by its respective yearly mean:

for 2014:

mean = 21.8

indices: 0.72, 0.94, 1.35

for 2015:

mean = 24

indices: 0.58, 0.97, 1.46

for 2016:

mean = 22.6

indices: 0.79, 0.86, 1.35

for 2017:

mean = 26.6

indices: 0.80, 0.93, 1.26

for 2018:

mean = 26.6

indices: 0.69, 1.02, 1.29

From the results we can see that every year indices are rising to the end of year.

2.

Deseasonalizing Data:

we divide each original profits figure by its respective quarterly index:

for 2014: 21.67, 21.70, 21.78

for 2015: 23.79, 23.92, 23.97

for 2016: 22.53, 22.56, 22.67

for 2017: 26.75, 26.67, 26.67

for 2018: 26.67, 26.67, 26.51

Thus, we smooth our profit data over the quarters.

3.

linear trend equation:

$y=ax+b$

where

$a=\frac{\sum y \sum x^2-\sum x\sum xy}{n\sum x^2-(\sum x)^2}$

$b=\frac{n\sum xy-\sum x\sum y}{n\sum x^2-(\sum x)^2}$

x is number of quarter,

y is profit.

So, the equation is

$y=0.4x+21$

We get increasing line with slope 0.4

4.

summer 2019 is II quarter of 2019

so, x=17

profit:

$y=0.4\cdot17+21=27.8$

Comparing with previous II quarters, profit will increasing.