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Statistics and Probability with Applications for Engineers and Scientists by Irwin Guttman, Bhisham C. Gupta

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15

Simple Linear Regression Analysis

The focus of this chapter is the development of some procedures employed in simple linear regression analysis.

Topics Covered:

  • Basic concepts of regression analysis
  • Fitting a straight line by least squares
  • Unbiased estimation of error variance img
  • Tests and confidence intervals for the regression coefficients img of the simple linear regression model
  • Determination of confidence intervals for img
  • Determination of a prediction interval for a future observation Y
  • Inference about the correlation coefficient img
  • Residual analysis

Learning Outcomes:

After studying this chapter, the reader will be able to

  • Fit a simple linear regression model to a given set of data, and perform a residual analysis to check the validity of the model under consideration.
  • Estimate the regression coefficients using the method of least squares, and carry out hypothesis testing to test whether the first-order regression model is an appropriate fit to the given data.
  • Estimate the expected response, predict future observation values, and find their confidence intervals using the given confidence ...

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