Q1. Scenerio: 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 (a cap) 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. 1. What is the explanatory variable (x-axis) and what is the response variable (y-axis)? 2. What is the best linear equation for predicting sales based on marketing spend? I.e. what are the intercept and slope terms? 3. What is the correlation between marketing spend and sales? 4. How much of the variation in sales is explained by marketing spend? I.e. what is the coefficient of determination, r2? 5. What is the standard error, se? 6. Produce 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. 7. About how many points would be expect to see more than 2se from the line? How many are there actually? 8. Linear regression makes some quite strong assumptions about the data including that:

i. The variation around the line, i.e. the error term, should be the same everywhere. ii. The mean values of the response variable for different values of the explanatory variable should fall on a straight line. How well does the data set meets the assumptions above? Name one other assumption made by linear regression. 9. Based on your model what would be the predicted sales for an item where you spent 500 bitcoins on marketing? Discuss how precise you expect this prediction to be. 10. On the basis of the calculation above, do you think it is worth using the Instagram influencer to market your products? 11. 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?

Q2. Scenario: Concerns have been raised about the effectiveness of this season's flu vaccination after it was noticed that a high proportion of people with severe illness have been vaccinated. Data has been collected on the following attributes of the flu sufferers.

ID - An identification number for the individual with flu AGE - The person's age in years VAC STATUS - Whether or not the person has been vaccinated against the flu SEVERITY - The severity of the illness (mild or severe) AGE CAT - A categorical version of the age variable with 5 bins (0-20, 21-40, 41-60, 61-80, 80+) The role is to investigate the data to determine if vaccination is effective or not 1. What percentage of vaccinated and unvaccinated people experience severe illness? 2. What is the average age of patients that are severely ill compared to patients with mild illness? 3. What is the average age of people that are vaccinated compared to people that are unvaccinated? 4. What proportion of people in the age category 41-60 are vaccinated? 5. Is there any age category where a higher proportion of vaccinated people are severely ill compared unvaccinated people? 6. Based on the investigation of the data set create two well-formatted tables that illustrate some important features of the data. (The tables should have informative labels and a readable number of decimal places. Each table should include an informative caption) 7. With reference to the tables that have been made, explain if there is evidence that the vaccine is effective or not? 8. One reason why it is difficult to ascertain cause and effect based on association is that there may be confounding variables, these are variables which are related to both the explanatory (independent) and response (dependent) variable. In the data set presented here which variable is explanatory, which is response, and which is confounding?

9. Imagine that the data is this study has been collected by surveying people who present at hospital with flu symptoms. Can you identify any potential biases in this form of data collection that might influence our ability to answer our key question? How else could data be collected to avoid this bias?