Let the given time series data showing quarterly sales of dishwashers at Big Boys Appliances over past two years:
Time Sales
2010 Quarter 1 20
2010 Quarter 2 85
2010 Quarter 3 64
2010 Quarter 4 30
2011 Quarter 1 70
2011 Quarter 2 125
2011 Quarter 3 105
2011 Quarter 4 90
The scatter plot of data above illustrates seasonality with trend. Therefore, a time-series regression model with trend and seasonality must be run to forecast demand.
We denote sales (Y) as depend variable, and denote time (t) and seasonality dummy variables (S_2, S_3, and S_4) as independent variables. Here, we select quarter 1 as baseline and adopt three seasonality dummy variables, such that S_2=1 represents quarter 2, S_3=1 represents quarter 3, and S_4=1 represents quarter 4. Answer the given questions.
A. Use above variable definition to code data above.
Time Sales(Y) Time (t) S_2 S_3 S_4
2010 Quarter 1 20
2010 Quarter 2 85
2010 Quarter 3 64
2010 Quarter 4 30
2011 Quarter 1 70
2011 Quarter 2 125
2011 Quarter 3 105
2011 Quarter 4 90
B. Copy data into Excel and run corresponding multiple regression. Write evaluated multiple regression equation use variables defined above.
C. Describe meaning of coefficients for time (t) and for seasonally dummy variable S_2. Use actual variable name and numbers to answer questions.
D. Test overall fitness of model.
E. Which variables in current regression model are significant? And which are not significant? Justify the answer.