Question
(8,0 pontos )-Faca um ajuste exponencial , utilizando OS dados da tabela , pelo método dos minimos quadrados. square disappointed
Solution
3.3
(210 Votos)
Mário
Elite · Tutor por 8 anos
Resposta
### Faça um ajuste exponencial utilizando os dados da tabela pelo método dos mínimos quadrados para encontrar a equação na forma
.
Explicação
## Step 1: Understanding the Problem### The task is to perform an exponential fit using the least squares method on a given set of data. This involves finding an exponential function of the form
that best fits the data points in the table.## Step 2: Setting Up the Exponential Model### The exponential model we are fitting is
. To linearize this, we take the natural logarithm of both sides, resulting in
. This transforms the problem into a linear regression problem where
is the dependent variable and
is the independent variable.## Step 3: Applying the Least Squares Method### Using the least squares method, we need to find the values of
and
that minimize the sum of squared differences between the observed values
and the predicted values
. This involves solving the normal equations derived from the partial derivatives of the sum of squared errors with respect to
and
.## Step 4: Calculating Parameters### Calculate the necessary sums:
,
,
, and
. Use these to solve for
and
using the formulas:
where
is the number of data points.## Step 5: Exponentiating to Find 'a'### Once
is found, exponentiate it to get
:
.## Step 6: Formulating the Exponential Equation### Substitute the calculated values of
and
back into the exponential equation
to get the final fitted model.