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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

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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?

The time series plot suggests that there is upward trend in the sales. The graph also indicates the presence of regular systematic variation.

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

Coefficients Standard Error t Stat P-value
Intercept 1603.817 108.8358 14.73612 1.96E-21
T 63.16868 3.052805 20.69202 9.9E-29

Write the regression equation

Sales = 1603.817 +63.16868 * Time

Explain what the coefficient on Time tells you

The regression coefficient of time suggest that for a unit increase in time, the sales increase by 63.16868 units

Use this regression output to make a sales ...

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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