BEA140 Linear Regression Assignment

MODULE 2 – TOPIC 2 (LINEAR REGRESSION)

Tools required:

You are encouraged to complete the calculations for the regression analysis using built in Excel functions (as covered in the lectures and in computer lab 3).

Scenario.

You run an online business selling cosplay outfits based on popular TV series.

This season you have primarily relied on Facebook to advertise your different product lines. For 30 different similarly priced products you have kept records of the amount you spent (in bitcents) on marketing that item versus the quantity sold. In addition to your usual Facebook advertising you also tried a different approach to marketing one item (pictured right) where you hired an Instagram influencer. This cost 500 bitcents and you sold 263 items. Your task is to develop a linear model that can predict sales based on marketing spend. Subsequently, you want to evaluate if Instagram represents good value for money compared to your usual advertising approach.

Auto-graded questions

1. What is the explanatory variable (x-axis) and what is the response variable (y-axis)? [1 mark]
2. What is the best linear equation for predicting sales based on marketing spend? I.e. what are the intercept and slope terms? [1 mark]
3. What is the correlation between marketing spend and sales? [1 mark]
4. How much of the variation in sales is explained by marketing spend? I.e. what is the coefficient of determination, r2 ? [1 mark]
5. What is the standard error, se? [1 mark]

Questions for the manually-graded section of assignment

1. Create an appropriately formatted figure of the data, paying attention to labels and number formats. Include the line of best fit. The figure should also include an informative caption. [6 marks]
2. About how many points would you expect to see more than 2×se from the line? How many are there actually? [2 marks]
3. Linear regression makes some quite strong assumptions about the data including that:
   • The variation around the line, i.e. the error term, should be the same everywhere.
   • The mean values of the response variable for different values of the explanatory variable should fall on a straight line.
   
   How well do you think this data set meets the assumptions above? Name one other assumption made by linear regression. [3 marks]
4. Based on your model what would be the predicted sales for an item where you spent 500 bitcent on marketing? Discuss how precise you expect this prediction to be. [3 marks]
5. On the basis of the calculation above, do you think it is worth using the Instagram influencer to market your products? [2 marks]
6. You were about to go all in on advertising with the influencer but then became worried that the Thinking Cap may have sold more simply because it is cool rather than because it is being marketed more effectively. For the upcoming season you have 20 new products to market, what approach could you take to marketing them to tease out if Facebook or Instagram provides best value? [4 marks]

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