Statistics Solutions

(Solution Library) Savings-Mart sells patio and lawn furniture. Sales are seasonal, with higher sales during the spring and summer quarters and lower sales

Question: Savings-Mart sells patio and lawn furniture. Sales are seasonal, with higher sales during the spring and summer quarters and lower sales during fall and winter quarters. The company developed the following quarterly sales forecasting model using data from 2005Q1 to \(2009 \mathrm{Q} 4\) i.e. \(\mathrm{n}=20\) quarters:

\[\begin{matrix} \widehat{\text{Y}}\text{t}=8.25+0.125\text{t}-2.75\text{D}1\text{t}+0.25\text{D}2\text{t}+3.50\text{D}3\text{t} & {{\text{R}}^{2}}=0.789 & {} & {} \\ (2.5)\,(3.1)\,\,(1.8) & {} & {} & {} \\ \end{matrix}\]

where the numbers in parenthesis are t-values, \(\hat{\mathrm{Y}} \mathrm{t}=\) predicted quarterly sales (\$million) in quarter \(\mathrm{t}\) \(t=\) time period

D1 \(t=\) dummy variable \(=1\) for \(1^{\text {st }}\) quarter, 0 otherwise \(\mathrm{D} 2 \mathrm{t}=\) dummy variable \(=1\) for \(2^{\text {nd }}\) quarter, 0 otherwise \(\mathrm{D} 3 \mathrm{t}=\) dummy variable \(=1\) for \(3^{\text {rd }}\) quarter, 0 otherwise

  1. Explain what \(\mathrm{R}^{2}=0.789\) means.
  2. Forecast Savings-Mart's sales for each of the quarters in 2010 .
  3. Which variables of the model are statistically significant? Use t-test for \(\alpha=.05\).

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Solution: The downloadable solution consists of 2 pages
Deliverable: Word Document


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