STAT 210 1ST EditionGradeBuddyLecture 13Last Lecture: I. Relationship Between VariablesThis LectureII. Regression LineIII. ExtrapolationIV. ResidualV. Coefficient of determinationCurrent LectureVI. Regression line = equation of the line that best explains the relationship between X and YVII. Prediction: we can predict the value of Y for any value of X simply by substituting the value of X into the regression equationVIII. Y = intercept + slope(X)IX. Example: Example: weight = 6 + 10 * agea. At age = 4, we predict weight = 6 + 10 (4) = 6 +40 = 46 poundsX. Extrapolation – predicting outside the range of the original X data (this shouldbe avoided)XI. Example: If the data used to determine the regression equation weight = 6 +10 * age is only for kids between the ages of 2 and 10 (X between 2 and 10), then predicting the weight of a 45 year old is extrapolation: weight = 6 + 10(45) = 456 pounds.XII. Residual = the difference between an observed dependent variable (Y) value and a predicted dependent variable value.XIII. Residual = y-y hatXIV. How to do a residual plot: a. Compute the residual for each observation.b. Create a scatterplot with the independent variable (X) on the horizontal axis and the residuals on the vertical axis. XV. Ideal residual plot has points that are randomly scattered around 0 with no obvious patternXVI. Outliersa. One variable: an outlier is an observation that is significantly smaller or larger than the majority of the data.b. Two variables: an outlier is an observation that falls within the range of the data in the horizontal (X) direction but that lies far from the regression line in the vertical direction and hence produces a large residual.STAT 210 1ST EditionXVII. Observations which stand out from other observations in the horizontal (x) direction are called influential observationsXVIII. They usually have a large influence on the position of the regression lineXIX. Coefficient of Determination measures the proportion (fraction) of the total variation in the Y values that can be explained by the X values. So we want the coefficient of determination to be as large as