Problem 4. (20 points)

Consider the following time series data representing quarterly sales of dishwashers at Big Boys Appliances over the past two years:

Time	Sales
2010 Quarter 1	25
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 the data above shows seasonality with trend. Hence, a multiple regression model is run to forecast the demand. We denote sales (Y) as the depend variable, and denote time (t, with t=1 represent the first quarter of 2010) and dummy variables (S1, S2, and S3) as independent variables. Here, we choose quarter 4 as the baseline and adopt three seasonality dummy variables, such that S1=1 represents quarter 1, S2=1 represents quarter 2, and S3=1 represents quarter 3. Answer the following questions. Use =0.05.

1. (5 points) Use the above variable definition to code the data above.

Time	Sales(Y)	Time (t)	S1	S2	S3
2010 Quarter 1	25	1
2010 Quarter 2	85	2
2010 Quarter 3	64	3
2010 Quarter 4	30	4
2011 Quarter 1	70	5
2011 Quarter 2	125	6
2011 Quarter 3	105	7
2011 Quarter 4	90	8

1. (5 points) Copy all data into Excel and run the corresponding multiple regression. Write the estimated multiple regression equation use the variables defined above. (Hint: No need to conduct backwards elimination at this point.)

1. (5 points) Explain the meaning of the slopes for seasonally dummy variable S1, S2, and S3. (Note: Use actual variable name and numbers to answer the questions. Put numbers in the right context.)

1. (5 points) Test the overall fitness of the model. (State the hypotheses, and use Significant F to complete your test, use short version of 7 steps.)

(Bonus 5 points) Which variables in the current regression model are significant? And which are not significant? Justify your answer. (short version of 7 steps)