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.

Marketing	Sales
190	55
797	208
563	182
280	99
590	227
279	82
249	55
459	154
489	143
247	93
207	86
318	106
652	203
570	187
148	53
304	84
548	137
454	156
155	50
747	295
653	207
792	251
723	320
207	75
449	175
324	122
738	185
127	48
444	172
602	197

1. make a table of 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.

2. About how many points would you expect to see more than 2se from the line? How many are there actually?

a. Linear regression makes some quite strong assumptions about the data including that: b. The variation around the line, i.e. the error term, should be the same everywhere.

c.. 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. Based on your model what would be the predicted sales for an item where you spent 500 bitcoin on marketing? Discuss how precise you expect this prediction to be.

4. On the basis of the calculation above, do you think it is worth using the Instagram influencer to market your products?

5. 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?