Question

Year Quarter Sales ($000) 2015 1 $400 2015 2 2,000 2015 3 3,500 2015 4 260...

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, Q2, 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

  1. Use multiple regression models with dummy variables Q1, Q2, 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

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

Homework Answers

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

= 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

= 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.

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