Answer:
The answers to the question are
(a) The time series plot is given as attached
(b) The parameters for the line that minimizes MSE for the time series are;
y-intercept, b₀ = 19.993
Slope, b₁ = 1.77
MSE = 19.44
T = 19.993 + 1.774·t
(c) The average cost increase that the firm is realizing per year is $ 1.77
(d) The estimate of the cost/unit for next year is $35.96.
Step-by-step explanation:
(a) Using the provided data, the time series plot is given as attached
(b) Given hat the y-intercept, = b₀
Slope = b₁
Therefore the linear trend forecast equation is given s
T = b₀ + b₁·t
The linear trend line slope is given as
b₁ =
b₀ = - b₁·
Where:
Y = Time series plot value at t
n = Time period number
= Time series data average value and
= Average time, t
Therefore, =
= 4.5
=
= 27.975
Therefore the linear trend line equation T, is
b₁ = =
= 1.774
b₀ = - b₁·
= 27.975 - 1.774×4.5 = 19.993
Therefore the trend equation for the linear trend is
T = 19.993 + 1.774·t
MSE = =
= 19.44
(c) From the linear trend equation, the average is given as the slope of the curve or b₁ which is equal to 1.774
Therefore the average cost increase that the firm has been realizing per year is $ 1.77
(b) From the equation of the future trend, we have when y = 9
T is given as
T = 19.993 + 1.774×9 = 35.96
The cost/unit for 9th year is $35.96
