The linear regression model can be extended to forecast future values
The year at which the two trends will become equal is the year 1991
Reason:
Known parameters;
The given function that estimates the first trend is y = 5·x + 22.9
The given function that estimates the second trend is y = 3.3·x + 33
Where;
x = The number of years since 1985
Required:
The year when the two trends are equal
Solution:
The year when the two trends are equal is given by the point where the values of the functions are equal, which is found as follows;
Let, y₁ = 5·x + 22.9, and y₂ = 3.3·x + 33
When the two trends are equal, we have;
y₁ = y₂
Therefore;
5·x + 22.9 = 3.3·x + 33
Which gives;
5·x - 3.3·x = 33 - 22.9
1.7·x = 10.1
[tex]x = \dfrac{10.1}{1.7} = \dfrac{101}{17} \approx 5.94[/tex]
Therefore, the number of years since the 1985, after which the two trends become equal is x ≈ 5.94 which is approximately six years
Therefore, the two trends will be equal in approximately (1985 + 6) = 1991
The two trends will be equal in approximately the year 1991
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