A local store developed a multiplicative time-series model to forecast its revenues in future quarters, using quarterly data on its revenues during the 5-year period from 2008 to 2012. The following is the resulting regression equation: log10Y? = 6.102 + 0.012 X - 0.129 Q1 - 0.054 Q2 + 0.098 Q3 where Y? is the estimated number of contracts in a quarter X is the coded quarterly value with X = 0 in the first quarter of 2008 Q1 is a dummy variable equal to 1 in the first quarter of a year and 0 otherwise Q2 is a dummy variable equal to 1 in the second quarter of a year and 0 otherwise Q3 is a dummy variable equal to 1 in the third quarter of a year and 0 otherwise In testing the significance of the coefficient of X in the regression equation (0.012) which has a p-value of 0.0000. Which of the following is the best interpretation of this result? - The quarterly growth rate in revenues is not significantly different from 1.2% (? = 0.05). - The quarterly growth rate in revenues is significantly different from 0% (? = 0.05). - The quarterly growth rate in revenues is significantly different from 1.2% (? = 0.05). - The quarterly growth rate in revenues is not significantly different from 0% (? = 0.05).
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The coefficient of X in the regression equation is 0.012, which represents the quarterly growth rate in revenues. Show more…
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An economist wants to estimate a regression equation relating demand for a product (Y) to its price (X1) and income (X2). It is to be based on 12 years of quarterly data. However, it is known that demand for this product is seasonal; that is, it is higher at certain times of the year than others. a. One possibility for accounting for seasonality is to estimate the model: y = β0 + β1X1 + β2X2 + β3X3 + β4X4 + β5X5 + β6X6 + ε where X3, X4, X5, and X6 are dummy variable values, with: X3 = 1 in the first quarter of each year, 0 otherwise X4 = 1 in the second quarter of each year, 0 otherwise X5 = 1 in the third quarter of each year, 0 otherwise X6 = 1 in the fourth quarter of each year, 0 otherwise Explain why this model cannot be estimated by least squares. b. For a model that can be estimated as follows: y = β0 + β1X1 + β2X2 + β3X3 + β4X4 + β5X5 + ε Interpret the coefficients on the dummy variables in the model.
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