FANR 3000 1st Edition Lecture 11 Outline of Last Lecture I Determining Sample Size II Calculate Sample Size Outline of Current Lecture I Regression II Simple linear model III Hypothetical linear model IV Correlation V Coefficient of determination Current Lecture I II Regression Correlation and Causation y mx b Regression a functional relationship between two or more correlated variables that is often empirically determined by data and is used to predict the value of one variable when the values of other variables are known assuming causations o Regression is generally used for the purposes of prediction Dependent variable y the variable you want to predict you will only have one Independent variable x the variable s that you actually measure or use to explain the variation in the dependent variable Determine all of the predicted values and compare them to the actual sampled values Try to reduce the error term E Simple linear model y mx b y b0 b1x These notes represent a detailed interpretation of the professor s lecture GradeBuddy is best used as a supplement to your own notes not as a substitute Straight line that best fits a series of ordered pairs x y o Y predicted y value o b0 y axis intercept o b1 slope of the line Hypothetical linear model For true population Y b0 b1x E o b0 y axis intercept constant factor when x 0 y b0 can be positive negative or zero o b1 slope of the line the rate of change in y as x changes slope rise run o E random error in y Correlation Measures the strength and direction of the x and y relationship A strong relationship between x and y DOES NOT imply that x causes y no causation III IV V As x increases y increases in linear fashion Linear correlation coefficient r strength and direction of x y relationship o 1 r 1 o r all data points lie exactly in a straight line o r 0 8 is a strong correlation o r 0 5 is a weak correlation o r 0 has no correlation Coefficient of determination A measure of the strength of the linear relationship between the two variables Typically included with linear regression line Actually determining the amount of variability in your Y that is explained by you X 2 2 R or r Weak explanatory power 3 Moderate 3 6 The regression equation is not a perfect predictor of the independent variable unless all of the observations fall directly on the regression line Regression line thus serves as approximate predictor of the y variables for any given value of the x variable within the range of the observed x values