Question

Year	Quarter	Sales ($000)
2015	1	$400
2015	2	2,000
2015	3	3,500
2015	4	260
2016	1	740
2016	2	2,720
2016	3	4,900
2016	4	520
2017	1	1,500
2017	2	3,100
2017	3	6,520
2017	4	960
2018	1	1,840
2018	2	4,040
2018	3	7,680
2018	4	1,640
2019	1	3,520
2019	2	5,640
2019	3	8,900
2019	4	3,620

Problem 2

House Depot’s quarterly sales of a lawn, landscaping, and gardening items – like lawnmowers, fertilizers, lawn tractors, weed killers, etc. – The data is for the years 2015 thru 2019.

1. Construct a quarterly time-series plot of 5 years of data. Provide the plot below with appropriate names and titles. What type of pattern do you observe in the data?
2. Use multiple regression models with dummy variables Q₁, Q_2, and Q₃ to develop an equation to measure only the effects seasonality (no trend should be included). Use the following coding scheme to code the data.

• Dummy variable Q₁ takes a value of 1 if the data is for the first quarter. Otherwise, it is set at 0
• Dummy variable Q₂ takes a value of 1 if the data is for the second quarter. Otherwise, it is set at 0
• Dummy variable Q₃ takes a value of 1 if the data is for the third quarter. Otherwise, it is set at 0
• For the fourth quarter data, all the three dummy variables are set at 0.

Write the estimated regression equation below.

You need not show the computer output of the regression model. However, you need to comment on model results. What is the value of R²? What can you say about the value of significant F?

Provide the following forecasts using the model developed above. Fill in the values in the table provided.

	Year 2020	Year 2023
Quarter 1
Quarter 2
Quarter 3
Quarter 4

3. Use multiple regression models with dummy variables Q₁, Q_2, and Q₃ to develop an equation to measure the effects of seasonality and trend. To code, the data, use the same coding scheme as above.

                             

Write the estimated regression equation below.

You need not show the computer output of the regression model. However, you need to comment on model results. What is the value of R²? What can you say about the value of significant F?

Provide the following forecasts using the model developed above. Fill in the values in the table provided.

	Year 2020	Year 2023
Quarter 1
Quarter 2
Quarter 3
Quarter 4

4. Going forward, if you must use a model to forecast, which one would you use? Why?

Answer 1

1. The time series plot is:

There is a seasonal pattern with seasonality.

2. The estimated regression equation is:

y = 1400 + 200*Q1 + 2100*Q2 + 4900*Q3

R² = 0.662

The model is significant. (p = 0.0005 < 0.05)

	Year 2020	Year 2023
Quarter 1	1,600.0000	1,600.0000
Quarter 2	3,500.0000	3,500.0000
Quarter 3	6,300.0000	6,300.0000
Quarter 4	1,400.0000	1,400.0000

3. The estimated regression equation is:

y = -1402 + 900.5*Q1 + 2567*Q2 + 5133.5*Q3 + 233.5*t

R² = 0.960

The model is significant. (p = 0.0000 < 0.05)

	Year 2020	Year 2023
Quarter 1	4402	7204
Quarter 2	6302	9104
Quarter 3	9102	11904
Quarter 4	4202	7004

4. The model with a trend because it is including the year factor.