UVA STAT 2120 - Topic+02+Notes (3 pages)

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Topic+02+Notes



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Topic+02+Notes

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Pages:
3
School:
University Of Virginia
Course:
Stat 2120 - Introduction to Statistical Analysis

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STAT 2120 Notes on Topic 2 Least squares regression A regression line describes a one way linear relationship between variables o An explanatory variable explains variability in a response variable o Often one wants to predict from a given Such a prediction is denoted The least squares regression line makes the sum of squared prediction errors as small as possible o A prediction error is the vertical distance between a given point and a regression line o The formula for the least squares regression line is with slope and intercept Predictions are made by plugging in values of o Slope is the amount of change in when increases by one unit Intercept is the prediction at 0 o Calculate and by computer Properties of the least squares regression line o Interchanging and modifies the formulation o The line always passes through the point o The slope formula interprets the relationship in units of and through o Similarly measures the proportion of variability in that is explained by The residuals describe the leftover variation in after fitting the least squares regression line o Each residual is defined by o The average of the residuals is zero o Analysis of residuals helps to assess the suitability of a linear relationship o A residual plot is a scatterplot of residuals against the values of o The ideal residual plot should exhibit no systematic pattern patterns indicating a departure from the linear relationship are curvature trends in spread outliers in the residuals o An outlier in corresponds with an outlier in the residuals Such is observed as an observation that outside of the overall pattern of the relationship Influential observations are those whose individual deletion would have a strong impact on the regression line o An influential observation is often an outlier in but may not be an outlier in Cautions about correlation and regression Basic cautions o Correlation is for two way relationships regression for one way relationships o Only relevant for linear



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