Slide 1Practice ProblemsAdditional Reading and ExamplesTest 3Slide 5OutlierOutlierOutlierInfluential ObservationInfluential ObservationInfluential ObservationInfluential ObservationInfluential ObservationInfluential ObservationInfluential ObservationSlide 16Coefficient of DeterminationCoefficient of DeterminationCoefficient of DeterminationExample 30Example 30Example 30Motivating ExampleMotivating ExampleMotivating ExampleMotivating ExampleMotivating ExampleMotivating ExampleQuantitative VariablesE. Categorical DataCategorical DataCategorical DataMarginal DistributionCategorical DataExample 31Example 31Example 31Example 31Example 31Example 31Example 31Example 31Conditional DistributionConditional DistributionsConditional DistributionConditional DistributionsExample 32Example 32Example 32Example 32Example 32Example 32Example 32Simpson’s ParadoxSimpson’s ParadoxSlide 56Simpson’s ParadoxExample 33Example 33Example 33Example 33Example 33Example 33Example 33Example 33Example 33Example 33Example 33Example 33Example 33Example 33Example 33Slide 73STAT 210Lecture 17Describing Relationships Between VariablesOctober 5, 2016Practice ProblemsPages 130 through 137Relevant problems: V.12 through V.16Recommended problems: V.12, V.15 and V.16Additional Reading and ExamplesRead pages 127 – 129Test 3TOMORROW!!! Thursday, October 6Questions for the first 10 minutes, then test – papers due promptly at the end of class!Covers chapter 5 (pages 99 – 137)Combination of multiple choice questions and written/short answer questions and problems.Formulas provided; Bring a calculator!Practice Tests and Formula Sheet on Blackboard.ClickerOutlierOne variable: an outlier is an observation that is significantly smaller or larger than the majority of the data.Example: Ages of college students 18 19 19 20 22 22 23 25 27 70OutlierTwo 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.Outlier Outlier Large residualXYRange of X dataInfluential ObservationObservations which stand out from the other observations in the horizontal (X) direction are called influential observations.Influential observations usually have an unusually large influence on the position of the regression line.Influential ObservationXYInfluential ObservationXYInfluential ObservationXYInfluential ObservationXYInfluential ObservationXYInfluential ObservationXYInfluential observationClickerCoefficient of DeterminationMeasures 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 possible. Sxy2r2 = Sxx SyyCoefficient of Determinationr2 will always be between 0 and +1An r2 close to 1 implies that X explains most of the variation in Y and hence the regression line does a good job of predicting Y values from X.An r2 close to 0 indicates that the regression line is rather useless and that we should not put too much faith in the predicted values that result.Coefficient of DeterminationMeasures 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 possible.For example, if the correlation coefficient is r = .60, then the coefficient of determination is r2 = (.60)2 = .36, and hence the X variable explains approximately 36% of the variation in the Y variable.Example 30From example 26, r = .9192Example 30From example 26, r = .9192So r2 = (.9192)2 = .845Example 30From example 26, r = .9192So r2 = (.9192)2 = .845This implies that X = number of ads run explains roughly 84.5% of the variation in Y = number of cars sold.Motivating ExampleOften making good grades is associated with STUDYING, so we wish to analyze the relationship between time spent studying and grade on a test.Motivating ExampleA study is created to evaluate the effect that time spent studying has on the grade earned on a test.In this scenario, what are the independent and dependent variables?X = ???Y = ???Motivating ExampleA study is created to evaluate the effect that time spent studying has on the grade earned on a test.In this scenario, what are the independent and dependent variables?X = time spent studyingY = grade on testMotivating ExamplePredicted grade on test = 36 + 10(hours spent studying)Motivating ExamplePredicted grade on test = 36 + 10(hours spent studying)1. Are there any outliers or influential observations visible on the scatterplot? Clicker2. If the correlation coefficient is r = .82, calculate and interpret the coefficient of determination.Motivating ExamplePredicted grade on test = 36 + 10(hours spent studying)1. Are there any outliers or influential observations visible on the scatterplot? YES, an outlier at hours spent studying = 1.75, grade on the test = 100.2. If the correlation coefficient is r = .82, calculate and interpret the coefficient of determination.r2 = (.82)2 = .6724Hours spent studying explains approximately 67% of the variation in grade on the test.Quantitative VariablesEverything to this point has assumed two quantitative variables, an independent (or explanatory) variable X and a dependent (or response) variable Y. We have talked about how to describe the relationship between the two variables (direction, form and strength) and how the scatterplot, correlation coefficient and regression line can be used to help do this.E. Categorical DataNow suppose we have two qualitative or categorical variables: the variables vary in name, but not in magnitude, implying that they cannot be ranked.All we can do is name the categories and count the number of observations falling in each category.The question remains: is there a relationship between the two variables?Categorical DataWith two variables, we can count the number of observations that fall in each pair of categories. The counts are displayed in a two-way table.Categorical DataFreshman Sophomore Junior SeniorWarning 48 36 15 23Probation 29 42 12 14Good standing 71 37 18 62Marginal DistributionThere exists a marginal distribution for each variable.A marginal distribution lists the categories of the variable together with the frequency (count) or relative frequency (percentage) of observations in each category.Categorical
View Full Document
Unlocking...