continue expand. Nina, however, isn\'t certain that demand for their stereo unit
ID: 391063 • Letter: C
Question
continue expand. Nina, however, isn't certain that demand for their stereo units has grown with the number of joggers because of concern about jogging with earphones and competition from newer technologies. They have provided you with data for last year which is shown in the table below. Using least squares regression analysis, what would you estimate demand to be for Month 23? Last Year Sales 2135 1566 1877 2004 1359 1495 3053 1477 312 3057 1933 1747 2 4 7 8 10 12 If you create a graph in Excel and use the "add a trendline" function within the graphExplanation / Answer
Let’s assume that the linear trend equation for sales forecast is represented by the following equation
y = a + b *t…………………….. (1)
Where a is the y-intercept of the line and b is the slope of the line. Formula to calculate the a and b are following
Slop b = (n * ty – t * y) / {n * (t^2) - (t) ^2}
Intercept a = (y – b * t) / n
Where,
n is number of period = 12 (number of months)
y is the sum of total sales
t is the sum of months
ty is the sum of total sales * months
t^2 is the sum of squares of months
Now, Slop b = (n * ty – t * y) / {n * (t^2) - (t) ^2}
= (12 * 143471 – 78 * 22015) / (12 * 650 – 78^2) = 2.61
And Intercept a = (y – b * t) / n = (22015 – 0.93 * 78)/12 = 1817.61
Now putting the value of a & b in equation (1), we get
Y = 1817.61 + 2.61 * t
Sales for month 23 using the trend projection (linear regression) method, where t = 23
Y = 1817.61 + 2.61 * 23 = 1877.68
Therefore for Month 23 estimated demand is 1877.68.
Month (t) Sales (y) y*t t^2 1 2135 2135 1 2 1566 3132 4 3 1877 5631 9 4 2004 8016 16 5 1359 6795 25 6 1495 8970 36 7 3053 21371 49 8 1477 11816 64 9 312 2808 81 10 3057 30570 100 11 1933 21263 121 12 1747 20964 144 Sum 78 22015 143471 650Related Questions
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