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# Regression & Time Series Analysis

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

#### Solution Summary

The solution provides step by step method for the calculation of regression analysis and trend for a time series model. Formula for the calculation and Interpretations of the results are also included.

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