Please explain how to work the formula for the following.
Quarter Warehouse and Transportation Expense
1/2009 $12,500
2 11,300
3 11,600
4 13,700
1/2010 12,900
2 12,100
3 11,700
4 14,000
1/2011 13,300
2 12,300
3 12,100
4 14,600
The results of a simple regression analysis using all 12 data points yielded an intercept of $11,854.55 and a coefficient for the independent variable of $126.22 (R-squared =0.19, t = 1.5, SE = 974).
Calculate the quarterly forecasts for 2012 using the high–low method.
To calculate the quarterly forecasts for 2012 using the high-low method, follow these steps:
1. Identify the high and low values for the independent variable (time) and the dependent variable (warehouse and transportation expense). In this case, the independent variable is the quarter (1, 2, 3, 4), and the dependent variable is the warehouse and transportation expense.
2. Determine the difference between the high and low values for both the independent and dependent variables. For the independent variable, the high is Q4 2011 and the low is Q1 2009, so the difference is 3 years (12 quarters). For the dependent variable, the high is $14,600 and the low is $11,300, so the difference is $3,300.
3. Calculate the slope (or coefficient) of the regression equation. In this case, the slope is $126.22.
4. Use the slope to estimate the quarterly increase in warehouse and transportation expense. Divide the difference in the dependent variable ($3,300) by the difference in the independent variable (12 quarters) to get the estimated quarterly increase: $3,300 / 12 = $275.
5. Start with the expense in Q4 2011 ($14,600) and apply the estimated quarterly increase to forecast the expenses for the following quarters in 2012.
- For Q1 2012, add the estimated quarterly increase to Q4 2011: $14,600 + $275 = $14,875.
- For Q2 2012, add the estimated quarterly increase to Q1 2012: $14,875 + $275 = $15,150.
- For Q3 2012, add the estimated quarterly increase to Q2 2012: $15,150 + $275 = $15,425.
- For Q4 2012, add the estimated quarterly increase to Q3 2012: $15,425 + $275 = $15,700.
Therefore, the quarterly forecasts for 2012 using the high-low method are:
Q1 2012: $14,875
Q2 2012: $15,150
Q3 2012: $15,425
Q4 2012: $15,700