Math Problem Statement
he amount of coal used by a small town over several decades is given in the table below.
YearTons of Coal
1930
87.4
1940
144.9
1950
153
1960
140.5
1970
131.6
1980
166.1
1990
254.2
a) Perform regression to find a cubic polynomial that fits the data. Use years since 1930 as your inputs.
Solution
The cubic polynomial that fits the data is:
where is the number of years since 1930.
Would you like further details on how the regression was performed or any clarification on the results?
Here are 5 related questions for further exploration:
- What does each coefficient in the cubic polynomial represent in this context?
- How well does this cubic model fit the data?
- Can we use this model to predict coal consumption beyond 1990?
- What other types of regression models could be applied to this dataset?
- How would the polynomial change if we added more recent data points?
Tip: When fitting a polynomial to data, always check the residuals to evaluate how well the model fits.
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Math Problem Analysis
Mathematical Concepts
Regression Analysis
Cubic Polynomial
Data Fitting
Formulas
Cubic Polynomial: P(x) = ax^3 + bx^2 + cx + d
Regression Formula for Polynomial Fitting
Theorems
Least Squares Method
Suitable Grade Level
Grades 11-12 or College Level
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