For 2008-2014, a company has collected the following data on quarterly sales of its product.

a. The manager would like to know if there is an upward trend in sales of the product. Use the data above to estimate the quarterly trend in sales using a linear trend model of the form:

Q_t = a + bt.

Where Q_t = quarterly sales

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b. Does your statistical analysis indicate a trend? If so, is it an upward or downward trend and how great is it? Is it a statistically significant trend (use the 5 percent level of significance )?

c. Now adjust your statistical model to account for seasonal variation in sales. Estimate the following model of sales:

Qt= a  +  bt+  c₁D₁+  c₂ D₂+  c₃ D3

WhereD₁, D₂andD₃ are respectively dummy variables for quarters I, II, and III (e.g., D₁ is equal to 1 in the first quarter of each year and 0 in other quarters).

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d. Does the data indicate a statistically significantseasonal pattern (use the 5 percent level of significance)? If so, what is theseasonal pattern of sales of the product?

e. Comparing your estimates of the trend in sales in parts a and c, which estimate is likely to be more accurate? Why?

f. Using the estimated forecast equation from part c, forecast sales for quarter 1, 2, 3 and 4 of 2015; quarter 1, 2, 3, and 4 of quarter 16, and quarter 1 of 2017. What possible concerns do you have about these forecasts?