The ABX Company sells winter sports merchandise including skis, ice skates, sled
ID: 3340755 • Letter: T
Question
The ABX Company sells winter sports merchandise including skis, ice skates, sleds, and so on. Quarterly sales in thousands of dollars for ABX Company from first quarter of 1994 till fourth quarter of 2003 are used to analyze sales over this time period. A time series plot of the data and the output from fitting a linear trend variable as explanatory variable is reported below. The residual plot of the standardized residuals versus the fitted values and a time series plot of the standardized residuals is used to check the linear regression assumptions.
a)Is there a significant linear trend in this data? Justify your answer.
b)How much is the estimated average quarterly increase in Sales?
c)Give a 95% confidence interval for the average quarterly increase in Sales.
d)Does the time series plot of the standardized residuals indicate a pattern? If yes, what kind of pattern? What is the implication?
Time Series Plot of SALES 320 300 280 260 240 220 200 QuarterQ1Q1Q1Q11Q1Q1Q1Q1Q1 Year 1994 1995 1996 19971998 19992000200120022003 The regression equation is SALES = 199 + 2.56 TIME predictor of SE coef Constant 199.017 5.128 38.81 0.000 TIME 2.5559 0.2180--- 8=15.9126 R-sa 78.3% R-Sq (adj) 77.0 = = Analysis of Variance DF MS Source Regression Residual Crror 3 9622 253 Total 1 34818 34818 137.50 0.000 39 44440 Versus Fits (resporse is SALES) Autocorrelation Function tor RESI ot iinear trend model (with 5% significance imits for the autocorrelations) 1.0 0.9 0.6 0.4 0.2 0.0 0.2 -0.5 0.8 1.0 10Explanation / Answer
a. Yes. There is significant trend in the data, by visual observation we can understand that there is upward trend exists in the data
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