A marketing researcher studied annual sales of a product that had been introduced 10 years ago....

  

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A marketing researcher studied annual sales of a product that had been introduced 10 years ago. The data are as follows, where X is the year (coded) and Y is sales in thousands of units: i: 1 2 3 4 5 6 7 8 9 10 X₁: 0 1 2 3 4 5 6 7 8 9 Y₁: 98 135 162 178 221 232 283 300 374 395 a. Prepare a scatter plot of the data. Does a linear relation appear adequate here? b. Use the Box-Cox procedure and standardization (3.36) to find an appropriate power transfor- mation of Y. Evaluate SSE for λ = .3, 4, 5, 6, .7. What transformation of Y is suggested? c. Use the transformation Y' = √Y and obtain the estimated linear regression function for the transformed data. d. Plot the estimated regression line and the transformed data. Does the regression line appear to be a good fit to the transformed data? e. Obtain the residuals and plot them against the fitted values. Also prepare a normal probability plot. What do your plots show? f. Express the estimated regression function in the original units. A marketing researcher studied annual sales of a product that had been introduced 10 years ago. The data are as follows, where X is the year (coded) and Y is sales in thousands of units: i: 1 2 3 4 5 6 7 8 9 10 X₁: 0 1 2 3 4 5 6 7 8 9 Y₁: 98 135 162 178 221 232 283 300 374 395 a. Prepare a scatter plot of the data. Does a linear relation appear adequate here? b. Use the Box-Cox procedure and standardization (3.36) to find an appropriate power transfor- mation of Y. Evaluate SSE for λ = .3, 4, 5, 6, .7. What transformation of Y is suggested? c. Use the transformation Y' = √Y and obtain the estimated linear regression function for the transformed data. d. Plot the estimated regression line and the transformed data. Does the regression line appear to be a good fit to the transformed data? e. Obtain the residuals and plot them against the fitted values. Also prepare a normal probability plot. What do your plots show? f. Express the estimated regression function in the original units.

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