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A few more things on LSRL Inference

This document outlines the inference conditions for Least Squares Regression Line (LSRL), focusing on a case study involving the estimation of bear weight based on body length. Key conditions include independent observations, a clear linear relationship indicated by scatterplot analysis, consistent standard deviation around the regression line, and normally distributed residuals. Using data from 143 bears, we determined a significant linear correlation, with a t-value of 20.17 and a p-value of 0.0001, leading us to reject the null hypothesis.

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A few more things on LSRL Inference

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  1. A few more things on LSRL Inference

  2. Conditions • Observations are independent • Scatterplot shows a possible linear relationship (residual plot has no obvious curve) • Standard deviation is consistent for all x.  Look at scatterplot. The scatter of the dots about the line should be roughly consistent.  Residuals are roughly evenly spaced around 0 in a residual plot. • Errors(residuals) around the regression line are normally distributed.  Probably will be given a normal probability plot of the residuals for this.  Make a stemplot of the residuals. (see pg 799)

  3. Example The fish and wildlife agency is interested in being able to estimate the weight of bears based on their length. Data was collected from a SRS of 143 bears and a LSRL regression line estimated. The output is given below: S = 56.07 R-sq = 74.3% R-sq(adj) = 74.1% Based on this information, is there a significant linear relationship between length of bear and its weight?

  4. Solution • Population is bears. Our hypotheses are: • Conditions are met: • Bears are selected independently • Scatterplot shows a general linear pattern. • Residuals are roughly consistent around 0 in the residual plot so we assume the standard deviation remains constant for all x. • Normal probability of the residuals indicates they are normally distributed

  5. Solution (3) We can get t = 20.17 directly from the print-out. The p-value for the 2 sided test is also there: p-value = .0001. (4) We reject the null as we have very strong evidence to state that there is a linear relationship between the length of a bear and its weight.

  6. HW • 14.14, 14.15

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