Time series

Trend

100

Name 3 types of trend descriptions

Upward/Increasing/positive

Downward/Decreasing/negative

Irregular

Seasonal

Cyclical

200

Describe the following graph

Upward/Increasing/positive.

Irregular OR Maybe Cyclical

300

What sort of trend would you expect to see for the amount of rain over the past 5 years?

Seasonal

400

Describe the trend of the graph below.

Seasonal and increasing

500

The graph below is about the rate of death due to alcohol.  Interpret the data below in terms of trend from 1997-2011.

The male death rate is decreasing from 1997 to 2011.  Then flat or slightly increasing from 2011 to 2017.  The female death rate is flat throughout. 

Smoothing

100

What are the 2 types of smoothing processes in time series graphs.

Moving averages

Deseasonalising

200

What is this formula calculating?

A seasonal index

300

What is the point of smoothing data?

To remove irregularities and determine long term trends.

400

Determine the 3-point moving average for day 5 (to the nearest whole number).

(710+730+790)/3=743

500

Calculate the seasonal index for the 3rd Quarter.

4-(1.4+0.7+0.88)=1.02

Seasonal Indices

100

A seasonal index of 1.15 for sales means that the season is;

a) 115% higher than average

b) 15% higher than average

c) 85% lower than average

d) 1.15 more than average

b) 15% higher than average

200

Calculate the seasonal index for the Sept quarter (2d.p)

=(120+145+155+134)/4=138.5

=155/138.5

=1.12

300

The deseasonalised sales figure for a particular month is $7809 and the seasonal index is 0.82.

What is the actual sales figure to nearest dollar?

deseasonalised data = actual data / SI

7809=actual data/0.82

0.82x7809= $6403

400

The seasonal index for Autumn is?

SI =(28.5+22.6+18.3+24.2)/4=23.4

Summer=28.5/23.4=1.22 

Autumn=22.6/23.4=0.97

500

Calculate the seasonal indices for each quarter

2017 yearly avg=(40+28)/2=34

2018 yearly avg=(44+25)/2=34.5

2019 yearly avg=(46+32)/2=39   

Q1 SI 40/34=1.18     44/34.5=1.28    46/39= 1.18 

Q1 SI avg. (1.18+1.28+1.18)/3=1.21

same process for Q2

Bivariate Data

100

The general equation for the least squares line of regression is;

y=a+bx

200

a and b stand for what variables

a is the y-intercept

b is the gradient/slope

300

R² stands for what variable

The coefficient of determination

400

r stands for what variable

The correlation coefficient 

500

Calculate the least squares line of regression for the following data;

a= 8547.5

b= -1827.8

y=a + bx

y=8547-1828x