The accompanying dataset contains six years of quarterly sales from your store. You would like to forecast future sales as way to inform you as you make staffing and budgeting plans. Please answer all of the following questions. The dataset can be found here.
For numerical questions, answer with 4 digits to the right of the decimal.
Statistically test at the alpha=0.05 statistical significance level whether or not there exists a linear trend in the time series data. What is the p-value of your statistical test?
Based on your answer to the question above, can you conclude that a linear trend exists in this time series data (Y or N)?
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Regardless of you answer above, create a multiple linear regression model that captures both linear trend and additive seasonality. You should use Q4 as your base season and fit the model with all 24 data points.
All of the independent variables are statistically significant at the alpha=0.01 level (Y or N).
Which quarter (1, 2, 3, or 4) has the largest sales on average?
Which quarter (1, 2, 3, or 4) has the smallest sales on average?
What is the value of the Adjusted R-squared?
Using this multiple linear regression model, what is the value of the MAPE? (Please report it as a percentage with 4 digits to the right of the decimal and no percentage sign.)
Using this multiple linear regression model, forecast each quarter for the next year (2016). What is the forecast for Q3?
Carefully explain the how to interpret the value of the estimated coefficient on the time period index.
Carefully explain the how to interpret the value of the estimated coefficient on the variable representing quarter one.
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Using the same dataset as before, you now would like to add an exogenous variable as a possible explanatory variable to the model. This variable is in the column labeled ‘Ads – Lag 1’. This variable represents the number of advertising campaigns ran the previous quarter. (The thought is that the ads run last quarter affect the current quarter’s sales.)
Calculate the correlation coefficient between the variables ‘Ads – Lag 1’ and ‘Sales’. What is its value?
Continuing with this thought, now create a multiple linear regression model that captures both linear trend and additive seasonality. You should use Q4 as your base season and fit the model with all 24 data points. Additionally, add the variable ‘Ads – Lag 1` as an independent variable.
Is the variable ‘Ads – Lag 1` statistically significant at the alpha=0.05 level (Y or N)?
What is the value of the Adjusted R-squared value?
0.4699
Using this multiple linear regression model that captures trend and additive seasonality and the additional independent variable for advertising, what is the value of the MAPE? (Please report it as a percentage with 4 digits to the right of the decimal and no percentage sign.)
Using only the data that you have been given, can you make forecasts for the year 2016 using this model (Y or N)?
If your answer was “Y” above, then what is the forecast for Q1 of 2016. If it was “N”, explain why not.
Solved by A. J. in 18 mins