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STAT2509 ClassNotes

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STAT 2509

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Simple Linear Regression notesSLR MODELPopulation or Estimated model using sample valuesy is the outcome response variable x is the explanatory variable5 Assumptions of the SLR model 1 LLINEARThe relationship between x and y is linearValidated by checking scatter plot of X vs Y 2 IINDEPENDENCExvalues are INDEPENDENT of each other so that y andvalues are INDEPENDENTLY DISTRIBUTED with means and xvalues are OBSERVED WITHOUT ERROR for both y and Plot y vs residuals e to check violations of INDEPENDENCEi3 N NORMAL DISTRIBUTIONyvalues are NORMALLY DISTRIBUTED with N andfor every value of x values areN Plot histogram of residuale frequencies to check violations of NORMAL distribution of ierrors Skewed indicates problem24 E EQUAL VARIANCEyvalues have CONSTANT VARIANCEfor any given value of x 2values have constant variancefor any given value of xPlot x vs residuals e to check violations of CONSTANT VARIANCE i ztestfor POPULATIONttest H 0 01H0 a1 Twotailedtest for 2 Dfn2 Reject H if Ttest value tn22 or Ttest valuetn22 0ConclusionAt a 5 level of significance there is evidence of a linear relationship between x and yOnetailed testH EyH EyRR t tn22 00a0 H EyH EyRR t tn22 00a0 CONFIDENCE INTERVALS1 Make sure that the interval does not BOUND ZEROotherwise there is a risk the slope could be 0 If CI does not bound 0 thenevidence of linear relationshipConclusion I am 95 confident that in repeated sampling the true population slopewould lie in the 1interval aa Page 1 of 6
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