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Consider the model = bx+ ε , where a and b are

constants and ε is the error term. Explain how you would estimate
parameters a and b.

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2 votes

Final answer:

To estimate the parameters a and b in the linear model y = bx + ε, use the method of least squares to minimize the sum of squared errors (SSE) and calculate the best-fit line.

Step-by-step explanation:

The model y = bx + ε, where a and b are constants and ε is the error term, represents a simple linear regression analysis. Estimating parameters a and b is crucial in determining the best-fit line for a given set of data. To estimate these parameters, one typically uses the method of least squares.

Here is a brief overview of the steps involved in estimation:

  • Draw a scatter plot of the data.
  • Calculate the least-squares line by using calculus to minimize the sum of squared errors (SSE).
  • Write the equation of the line in the form ý = a + bx, where ý is the estimated value of y.
  • Calculate the correlation coefficient to assess the strength of the linear relationship.

The constants a and b can be computed using formulas that derive from minimizing the SSE. Specifically, b represents the slope, which is determined by the change in y over the change in x, while a is the y-intercept of the regression line.

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