The table below shows annual demand (in 1,000,000 units per year) for Widgets. Use this information to calculate a constant growth forecasting model. Use your growth model to forecast demand for the years 1995 and 2000.
Year Demand
1990 1.1
1991 1.5
1992 1.5
1993 1.8
All help is appreciated, considering the professor never taught us what a 'constant growth model' is.
Here the linear regression equation is Y=0.95+0.24t where Y= the output and t=the time.Hence the output in 1995 is
Y=0.95+(0.24).6=2.9
Output in 2000 is Y=0.95+(0.24).11=3.59
So, a constant growth forcasting model is the same as a linear forecasting model ?
A constant growth forecasting model, also known as a linear forecasting model, assumes that the demand for widgets increases at a constant rate over time. This type of model assumes a linear relationship between the year and the demand for widgets.
To calculate a constant growth forecasting model, we can use linear regression to find the equation of the line that best fits the given data points. The linear regression equation is typically in the form Y = a + bt, where Y represents the output (demand for widgets) and t represents the time (in this case, the year).
In this case, we have the following data points:
Year Demand
1990 1.1
1991 1.5
1992 1.5
1993 1.8
We can use these data points to calculate the values of a and b in the linear regression equation.
First, we need to calculate the average demand (Y) and the average year (t) from the given data points:
Average Y = (1.1 + 1.5 + 1.5 + 1.8) / 4 = 1.475
Average t = (1990 + 1991 + 1992 + 1993) / 4 = 1991.5
Next, we calculate the differences between each year and the average year and each demand value and the average demand:
t - average t Demand - average Y
1990 - 1991.5 = -1.5 1.1 - 1.475 = -0.375
1991 - 1991.5 = -0.5 1.5 - 1.475 = 0.025
1992 - 1991.5 = 0.5 1.5 - 1.475 = 0.025
1993 - 1991.5 = 1.5 1.8 - 1.475 = 0.325
Next, we calculate the sum of the products of the differences:
Sum of (t - average t) * (Demand - average Y) = (-1.5 * -0.375) + (-0.5 * 0.025) + (0.5 * 0.025) + (1.5 * 0.325) = 0.57
Next, we calculate the sum of the squares of the differences:
Sum of (t - average t)^2 = (-1.5)^2 + (-0.5)^2 + (0.5)^2 + (1.5)^2 = 4.5
Finally, we can calculate the values of a and b in the linear regression equation:
b = Sum of (t - average t) * (Demand - average Y) / Sum of (t - average t)^2
= 0.57 / 4.5
= 0.1267
a = average Y - b * average t
= 1.475 - (0.1267 * 1991.5)
= 1.475 - 252.5
= -251.025
So, the linear regression equation is:
Y = -251.025 + 0.1267t
To forecast the demand for the years 1995 and 2000, we can substitute the corresponding values of t into the equation:
For 1995 (t = 1995):
Y = -251.025 + 0.1267 * 1995
= 2.9
For 2000 (t = 2000):
Y = -251.025 + 0.1267 * 2000
= 3.59
Therefore, the constant growth forecasting model predicts that the demand for widgets in the year 1995 is approximately 2.9 million units per year and in the year 2000 is approximately 3.59 million units per year.