1 A forecaster used the following regression equation Qt = a + bt + c1D1 + c2D2 + c3D3 and quarterly sales data during 1999II to 2007IV (t = 1,...,35) for an appliance manufacturer to obtain the estimation results shown below. Q is quarterly sales, and D1, D2, and D3 are seasonal dummy variables for quarters I, II, and III. DEPENDENT VARIABLE: OBSERVATIONS: VARIABLE INTERCEPT T D1 D2 D3 QT RSQUARE FRATIO 35 0.9219 88.54 PVALUE ON F 0.0001 PARAMETER STANDARD ESTIMATE ERROR TRATIO 21.0 6.2 3.39 PVALUE 0.0019 0.90 8.0 6.0 4.0 0.0007 0.0043 0.0022 0.0001 0.24 2.60 1.80 0.60 3.75 3.08 3.33 6.67 a. Do the statistical estimates indicate a trend in sales? If so, what is the trend in units per quarter. Explain. b. What are the estimated intercepts for each of the four quarters? Explain. c. What level of sales are forecasted sales for the 1st, 2nd, 3rd, and 4th quarters of 2008? Explain. QUESTION 2 Seven teenagers, four boys and three girls, were given $200 each to go on a shopping spree. An advertising agency, which specializes in youth markets, gave the teens the money. An account executive accompanied the teens while they were shopping. The agency wanted to learn not only what they bought, but also what they talked about to see what was on their minds. "It's not so much to stay in tune with trends, because trends are elusive. It's more what's really happening with teens and what's important to them." [Source: "Teens Track Retail Trends for Ad Agency," Democrat and Chronicle (September 5, 1999), 1E.] a. Discuss the tradeoffs between sample size (7 teens), cost, and reliability of what is learned from this experiment. b. An agent accompanied the teens while they were shopping. Why didn't the ad agency avoid this expense and just look at what the teens bought? QUESTION 3 Cypress River Landscape Supply is a large wholesale supplier of landscaping materi als in Georgia. Cypress River's sales vary seasonally; sales tend to be higher in the spring months than in other months. a. Suppose Cypress River estimates a linear trend without accounting for this seasonal b. variation. What effect would this omission have on the estimated sales trend? c. Alternatively, suppose there is, in fact, no seasonal pattern to sales, and the trend line is estimated using dummy variables to account for seasonality. What effect d. would this have on the estimation? e