The function can be best modeled by a linear regression and the values of a, b and c are -6, 100 and 240, respectively
The function type
From the table, we can see that as the number of years increases, the population increases.
This implies that the function can be best modeled by a linear regression.
The values of a, b and c
A linear regression equation is represented by
ax + by = c
Next, we enter the data in a statistical calculator.
From the statistical calculator, we have the following summary:
- Sum of X = 225
- Sum of Y = 27.505
- Mean X = 37.5
- Mean Y = 4.5842
- Sum of squares (SSX) = 3937.5
- Sum of products (SP) = 231.4875
The regression equation is then represented as:
y = bx + a
Where:
b = SP/SSX = 231.49/3937.5 = 0.05879
a = MY - bMX = 4.58 - (0.06*37.5) = 2.37952
So, we have:
y = 0.05879x + 2.37952
Approximate
y = 0.06x + 2.4
Multiply through by 100
100y = 6x + 240
Rewrite as:
-6x + 100y = 240
Hence, the values of a, b and c are -6, 100 and 240, respectively
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