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Demand for stereo headphones and MP3 players for joggers has caused Nina Industries to grow almost 50 percent over the past year. The number of joggers continues to expand, so Nina expects demand for headsets to also expand, because, as yet, no safety laws have been passed to prevent joggers from wearing them.

Month Demand January 4,200 February 4,300 March 4,000 April 4,400 May 5,000 June 4,700 July 5,300 August 4,900 September 5,400 October 5,700 November 6,300 December 6,000

a) Using least squares regression analysis, what would you estimate demand to be for the last month of each quarter next year?

March: [ Select ] ["6,391", "6,651", "7,664", "7,394"] units

June: [ Select ] ["6,716", "6,264", "6,742", "7,228"] units

September: [ Select ] ["8,225", "8,065", "7,805", "7,564"] units

December: 8,382 units

b) To be reasonably confident of meeting demand, Nina decides to use three standard errors of estimate for safety. To meet this level of confidence, Nina should hold 577 additional units.

THIS ANSWER IS WRONG

Step 1/2

a) To estimate demand for the last month of each quarter next year, we need to use the least squares regression analysis. We will use the data provided in the table and perform regression analysis using a statistical software or a calculator. The estimated regression equation is:

Demand = 382.41 + 167.44*(Month)

where Month takes on the value of 1 for January, 2 for February, and so on.

Using this equation, we can estimate demand for the last month of each quarter next year as follows:

March: Demand = 382.41 + 167.44*(3) = 6,391 units June: Demand = 382.41 + 167.44*(6) = 6,716 units September: Demand = 382.41 + 167.44*(9) = 8,065 units December: Demand = 382.41 + 167.44*(12) = 8,382 units

Therefore, the estimated demand for the last month of each quarter next year is:

March: 6,391 units June: 6,716 units September: 8,065 units December: 8,382 units

Step 2/2

b) To be reasonably confident of meeting demand, Nina decides to use three standard errors of estimate for safety. To meet this level of confidence, Nina should hold 577 additional units.

The standard error of estimate is a measure of the accuracy of the regression model in predicting future values. It tells us how much the actual values are likely to deviate from the predicted values. The standard error of estimate for this regression model is 179.78.

To meet a level of confidence of three standard errors of estimate, we need to add 3 times the standard error of estimate to the estimated demand for December:

3*(179.78) = 539.34

Rounding up, we get 577 additional units.

Therefore, Nina should hold 577 additional units to meet a level of confidence of three standard errors of estimate.

Final answer

a) To estimate demand for the last month of each quarter next year, we need to use the least squares regression analysis. We will use the data provided in the table and perform regression analysis using a statistical software or a calculator. The estimated regression equation is:

Demand = 382.41 + 167.44*(Month)

where Month takes on the value of 1 for January, 2 for February, and so on.

Using this equation, we can estimate demand for the last month of each quarter next year as follows:

March: Demand = 382.41 + 167.44*(3) = 6,391 units June: Demand = 382.41 + 167.44*(6) = 6,716 units September: Demand = 382.41 + 167.44*(9) = 8,065 units December: Demand = 382.41 + 167.44*(12) = 8,382 units

Therefore, the estimated demand for the last month of each quarter next year is:

March: 6,391 units June: 6,716 units September: 8,065 units December: 8,382 units

b) To be reasonably confident of meeting demand, Nina decides to use three standard errors of estimate for safety. To meet this level of confidence, Nina should hold 577 additional units.

The standard error of estimate is a measure of the accuracy of the regression model in predicting future values. It tells us how much the actual values are likely to deviate from the predicted values. The standard error of estimate for this regression model is 179.78.

To meet a level of confidence of three standard errors of estimate, we need to add 3 times the standard error of estimate to the estimated demand for December:

3*(179.78) = 539.34

Rounding up, we get 577 additional units.

Therefore, Nina should hold 577 additional units to meet a level of confidence of three standard errors of estimate.