i) To find the trend equation of the sales of General Electronics, we can use the method of least squares. The general form of the trend equation is Y = a + bX, where Y is the dependent variable (sales), X is the independent variable (year), a is the Y-intercept, and b is the slope of the line.

First, we need to calculate the values of X (which is the year minus the base year 2015), Y (which is the sales), XY, and X^2. Then, we sum up these values.

Next, we substitute these sums into the formulas for a and b:

a = (ΣY - bΣX) / n
b = (nΣXY - ΣXΣY) / (nΣX^2 - (ΣX)^2)

After calculating a and b, we can write the trend equation.

ii) To forecast the sales for the year 2024, we substitute X = 2024 - 2015 = 9 into the trend equation.

iii) The growth rate can be calculated as (Sales2022 - Sales2015) / Sales2015 * 100%. The acceleration rate can be calculated as (Growth rate2022 - Growth rate2015) / Growth rate2015 * 100%.

iv) The trend equation shows the general direction of the sales over the years. The forecasted sales for 2024 gives an estimate of the sales in that year based on the trend. The growth rate shows the percentage increase in sales from 2015 to 2022, and the acceleration rate shows the percentage increase in the growth rate over the same period. These results can help the company in planning and decision making.

Please note that the actual calculations depend on the specific data given, and the above steps are a general guide.

Question

i) To find the trend equation of the sales of General Electronics, we can use the method of least squares. The general form of the trend equation is Y = a + bX, where Y is the dependent variable (sales), X is the independent variable (year), a is the Y-intercept, and b is the slope of the line.

First, we need to calculate the values of X (which is the year minus the base year 2015), Y (which is the sales), XY, and X^2. Then, we sum up these values.

Next, we substitute these sums into the formulas for a and b:

a = (ΣY - bΣX) / n
b = (nΣXY - ΣXΣY) / (nΣX^2 - (ΣX)^2)

After calculating a and b, we can write the trend equation.

ii) To forecast the sales for the year 2024, we substitute X = 2024 - 2015 = 9 into the trend equation.

iii) The growth rate can be calculated as (Sales2022 - Sales2015) / Sales2015 * 100%. The acceleration rate can be calculated as (Growth rate2022 - Growth rate2015) / Growth rate2015 * 100%.

iv) The trend equation shows the general direction of the sales over the years. The forecasted sales for 2024 gives an estimate of the sales in that year based on the trend. The growth rate shows the percentage increase in sales from 2015 to 2022, and the acceleration rate shows the percentage increase in the growth rate over the same period. These results can help the company in planning and decision making.

Please note that the actual calculations depend on the specific data given, and the above steps are a general guide.

Knowee AI · Accepted Answer

i) To find the trend equation of the sales of General Electronics, we can use the method of least squares. The general form of the trend equation is Y = a + bX, where Y is the dependent variable (sales), X is the independent variable (year), a is the Y-intercept, and b is the slope of the line.

First, we need to calculate the values of X (which is the year minus the base year 2015), Y (which is the sales), XY, and X^2. Then, we sum up these values.

Next, we substitute these sums into the formulas for a and b:

a = (ΣY - bΣX) / n
b = (nΣXY - ΣXΣY) / (nΣX^2 - (ΣX)^2)

After calculating a and b, we can write the trend equation.

ii) To forecast the sales for the year 2024, we substitute X = 2024 - 2015 = 9 into the trend equation.

iii) The growth rate can be calculated as (Sales2022 - Sales2015) / Sales2015 * 100%. The acceleration rate can be calculated as (Growth rate2022 - Growth rate2015) / Growth rate2015 * 100%.

iv) The trend equation shows the general direction of the sales over the years. The forecasted sales for 2024 gives an estimate of the sales in that year based on the trend. The growth rate shows the percentage increase in sales from 2015 to 2022, and the acceleration rate shows the percentage increase in the growth rate over the same period. These results can help the company in planning and decision making.

Please note that the actual calculations depend on the specific data given, and the above steps are a general guide.

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