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# intercept in each of the four quarters

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This solution calculates the intercept in each of the four quarters. What do these values imply in terms about the presence of seasonality in sales?

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https://brainmass.com/economics/estimation-and-forecasting/intercept-in-each-of-the-four-quarters-430107

#### Solution Preview

See the attached file.

Consider a firm subject to quarter-to-quarter variation in its sales. Suppose that the following equation was estimated using quarterly data for the period 2000-2009 (the time variable goes from 1 to 37). The variables D1, D2 and D3, are respectively, dummy variables for the first, second, and third quarters (e.g., D1 is equal to one in the first quarter and zero otherwise).
Q1 + a + bt + c1D1 + c2D2 +c3D3
The results of the estimation are presented below:
DEPENDENT VARIABLE : QT F-RATIO: 761.133

OBSERVATIONS: 36 R2: 0.9761

PARAMETER STANDARD
VARIABLE ESTIMATE ...

#### Solution Summary

The presence of seasonality in sales is clearly assessed in this solution.

\$2.19

## Quantitative Analysis and Data Management

The problem set has been attached. It has to do with Regression and forecasting.

Create a graph of Sales over this time period (Quarter 1 of 1986 through Quarter 1 of 2001)

What do you see happening to Coca Cola sales over this time period?

Run a simple linear regression of Sales on Time Period (recode the time period variable to be period 1-61).
Write the regression equation

Explain what the coefficient on Time tells you

Use this regression output to make a sales forecast for the time period below, if you assume that seasonality and time trends are additive.
Forecasted Sales for Quarter 3 of 2002 =
Use this regression output to make a sale forecast for the time period below, if you assume that seasonality and time trends are multiplicative.
Forecasted Sales for Quarter 3 of 2002 =
Run a multiple linear regression of Sales on Time Period and Season (where season is capture in dummy variables for each quarter). Include variables for quarters 1, 2 and 3 in your regression (so quarter 4 is your reference group).
Write the regression equation
Explain what the coefficients tell you.
The coefficient on time tells me that
The coefficient on Quarter 1 tells me that
The coefficient on Quarter 2 tells me that
The coefficient on Quarter 3 tells me that
Use this regression output to make a sales forecast for the time period below.
Forecasted Sales for Quarter 3 of 2002 =
Now run a multiple linear regression of Sales on Time Period and Season (where season is capture in dummy variables for each quarter). Include variables for quarters 1, 2 and 4 in your regression (so quarter 3 is your reference group).
Use this regression output to make a sales forecast for the time period below.
Forecasted Sales for Quarter 3 of 2002 =

Data set

Coca Cola quarterly sales

Quarter Sales
Q1-86 1734.83
Q2-86 2244.96
Q3-86 2533.80
Q4-86 2154.96
Q1-87 1547.82
Q2-87 2104.41
Q3-87 2014.36
Q4-87 1991.75
Q1-88 1869.05
Q2-88 2313.63
Q3-88 2128.32
Q4-88 2026.83
Q1-89 1910.60
Q2-89 2331.16
Q3-89 2206.55
Q4-89 2173.97
Q1-90 2148.28
Q2-90 2739.31
Q3-90 2792.75
Q4-90 2556.01
Q1-91 2480.97
Q2-91 3039.52
Q3-91 3172.12
Q4-91 2879.00
Q1-92 2772.00
Q2-92 3550.00
Q3-92 3508.00
Q4-92 3243.86
Q1-93 3056.00
Q2-93 3899.00
Q3-93 3629.00
Q4-93 3373.00
Q1-94 3352.00
Q2-94 4342.00
Q3-94 4461.00
Q4-94 4017.00
Q1-95 3854.00
Q2-95 4936.00
Q3-95 4895.00
Q4-95 4333.00
Q1-96 4194.00
Q2-96 5253.00
Q3-96 4656.00
Q4-96 4443.00
Q1-97 4138.00
Q2-97 5075.00
Q3-97 4954.00
Q4-97 4701.00
Q1-98 4457.00
Q2-98 5151.00
Q3-98 4747.00
Q4-98 4458.00
Q1-99 4428.00
Q2-99 5379.00
Q3-99 5195.00
Q4-99 4803.00
Q1-00 4391.00
Q2-00 5621.00
Q3-00 5543.00
Q4-00 4903.00
Q1-01 4479.00

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