Question

The data below shows the high temperatures on Washington's birthday from 2019 (temp. 25)-2010 (temp. 26). The independent variable is now 1-10 for the time-series model for forecasting.

Here is my questions:

1. Determine which variable from the time series forecast would be an appropriate dependent variable (X) and tell why.
2. Determine which variable from the time series forecast would be an appropriate independent variable (Y) and tell why.

If you could help me with this I would appreciate it, thank you!!!

Number of Periods Averaged	3					Analysis of Forecast Error
						MAD	MSE	MAPE
						11.39286	164.41964	43.16505%
Data
Period Number	Data		Indicates which cells in column to the right need a formula	Moving average forecast	error	absolute value of error	squared error	percentage error
1	25
2	39
3	59
4	26		Formula Needed -->	41.00000	-15.00000	15.00000	225.00000	57.69%
5	17		Formula Needed -->	37.25000	-20.25000	20.25000	410.06250	119.12%
6	30		Formula Needed -->	35.25000	-5.25000	5.25000	27.56250	17.50%
7	49		Formula Needed -->	33.00000	16.00000	16.00000	256.00000	32.65%
8	40		Formula Needed -->	30.50000	9.50000	9.50000	90.25000	23.75%
9	32		Formula Needed -->	34.00000	-2.00000	2.00000	4.00000	6.25%
10	26		Formula Needed -->	37.75000	-11.75000	11.75000	138.06250	45.19%
11			Formula Needed -->	36.75000

Answer 1

For the given data on high temperatures on Washington's birthday and keeping in mind the Forecasting problem:

a) The dependent variable (X) is the unknown value of high temperatures in the future period i.e. for the period onwards 2020 as per the given problem. The data for 2010-2019 is already given and hence, we use this data to forecast the temperature for later periods. Hence the appropriate dependent variable is high temperatures from periods after 2019.

b) Independent variable is the value of the same time series in previous time steps. Weighted average of the previous observations gives the moving average forecast for the future values. Hence the data for 2010-2019 acts as independent variable. Also, sometimes the forecasted values are also used as independent variable for the future forecasts.