Multiple linear regression question . The following sales data were collected fo
ID: 3225928 • Letter: M
Question
Multiple linear regression question.
The following sales data were collected for one particular product from a company for the past 10 seasons. The data are the price of the product that the company itself charged, the price that its competitor charged (for the competitor’s version of the same product), the corresponding sales of the company’s product, and the season.
Answer the following questions completely!!! You don’t need to use software. The paramters for the model have already been estimated. Just use the output provided above.
(a) Interpret each of the model parameters 0, 1, 2, and 3. By “interpret”, I mean numerically interpret the estimated parameters. For example, what does 0 = 97.8067 represent?
(b) Do you think that competitor price should be included in the model? Explain the reasoning for your answer.
(c) What is the expected company sales if the company and the competitor both set their prices to $11 for the winter season? Use the full model, regardless of your answer to part 1b
(d) Would you use this model to predict company sales at a price of $15 for either season? Explain the reasoning for your answer.
company price competitor price sales (1000s) season $10.2 S9.9 71.1 winter 11.6 63.0 summer 11.7 71.7 winter 9.8 13.7 9.5 58.3 summer 8.9 12.0 61.8 summer 10.1 11.2 66.0 summer 10.2 11.1 71.2 winter 10.6 10.7 66.9 winter 9.5 12.6 72.5 winter 11.8 10.0 65.4 winter Here is a plot of the data. Season is not shown.Explanation / Answer
Part-a
0 = 97.8067 which means that when competitor and company price are zero in winter season the sales is 97807 which I smeaning less as price can never be zero
1 = -2.9269 which means that corresponding to $ 1 increase in company price there is on an average a decrease of 2927 in sales, holding competitor price and season as fixed
2 = 0.2078 which means that corresponding to $ 1 increase in competitor price there is on an average an increase of 208 in sales, holding company price and season as fixed
3 = -2.0388 which means that for summer season there is on an average 2039 lower sales as comapred to winter season, holding company price competitor price as fixed
Part-b
No, it should not be included in model as its coefficient is non-significant with p-value=0.74407>0.05.
Part-c
Expected company sales =1000*(97.8067-2.9269*11+0.2078*11-2.0388*0)
=67896.6
=67897
Part-d
No, because this price is out of range of the given data.
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