IntroductionScatterplotsDescribing RelationshipsScatterplots on the TI-83Linear RegressionWhich Line is Better?Measuring the Goodness of FitAssignmentModeling a Linear RelationshipLecture 41Sections 13.1 - 13.3.1Robb T. KoetherHampden-Sydney CollegeWed, Nov 9, 2011Robb T. Koether (Hampden-Sydney College) Modeling a Linear Relationship Wed, Nov 9, 2011 1 / 49Outline1Introduction2Scatterplots3Describing Relationships4Scatterplots on the TI-835Linear RegressionWhich Line is Better?Measuring the Goodness of Fit6AssignmentRobb T. Koether (Hampden-Sydney College) Modeling a Linear Relationship Wed, Nov 9, 2011 2 / 49Outline1Introduction2Scatterplots3Describing Relationships4Scatterplots on the TI-835Linear RegressionWhich Line is Better?Measuring the Goodness of Fit6AssignmentRobb T. Koether (Hampden-Sydney College) Modeling a Linear Relationship Wed, Nov 9, 2011 3 / 49IntroductionIn Chapter 13, we will investigate the relationship between twoquantitative variables.In Chapter 14, we will investigate the relationship between two ormore qualitative variables.In Chapter 13, the basic problems will beDetermine whether there is a relationship.If there is one, then describe it quantitatively.Through this quantitative description, we will to be able to predictthe value of one variable when we know the value of the other.Robb T. Koether (Hampden-Sydney College) Modeling a Linear Relationship Wed, Nov 9, 2011 4 / 49IntroductionIn Chapter 13, we will investigate the relationship between twoquantitative variables.In Chapter 14, we will investigate the relationship between two ormore qualitative variables.In Chapter 13, the basic problems will beDetermine whether there is a relationship.If there is one, then describe it quantitatively.Through this quantitative description, we will to be able to predictthe value of one variable when we know the value of the other.Robb T. Koether (Hampden-Sydney College) Modeling a Linear Relationship Wed, Nov 9, 2011 4 / 49IntroductionIn Chapter 13, we will investigate the relationship between twoquantitative variables.In Chapter 14, we will investigate the relationship between two ormore qualitative variables.In Chapter 13, the basic problems will beDetermine whether there is a relationship.If there is one, then describe it quantitatively.Through this quantitative description, we will to be able to predictthe value of one variable when we know the value of the other.Robb T. Koether (Hampden-Sydney College) Modeling a Linear Relationship Wed, Nov 9, 2011 4 / 49IntroductionIn Chapter 13, we will investigate the relationship between twoquantitative variables.In Chapter 14, we will investigate the relationship between two ormore qualitative variables.In Chapter 13, the basic problems will beDetermine whether there is a relationship.If there is one, then describe it quantitatively.Through this quantitative description, we will to be able to predictthe value of one variable when we know the value of the other.Robb T. Koether (Hampden-Sydney College) Modeling a Linear Relationship Wed, Nov 9, 2011 4 / 49IntroductionIn Chapter 13, we will investigate the relationship between twoquantitative variables.In Chapter 14, we will investigate the relationship between two ormore qualitative variables.In Chapter 13, the basic problems will beDetermine whether there is a relationship.If there is one, then describe it quantitatively.Through this quantitative description, we will to be able to predictthe value of one variable when we know the value of the other.Robb T. Koether (Hampden-Sydney College) Modeling a Linear Relationship Wed, Nov 9, 2011 4 / 49IntroductionIn Chapter 13, we will investigate the relationship between twoquantitative variables.In Chapter 14, we will investigate the relationship between two ormore qualitative variables.In Chapter 13, the basic problems will beDetermine whether there is a relationship.If there is one, then describe it quantitatively.Through this quantitative description, we will to be able to predictthe value of one variable when we know the value of the other.Robb T. Koether (Hampden-Sydney College) Modeling a Linear Relationship Wed, Nov 9, 2011 4 / 49Outline1Introduction2Scatterplots3Describing Relationships4Scatterplots on the TI-835Linear RegressionWhich Line is Better?Measuring the Goodness of Fit6AssignmentRobb T. Koether (Hampden-Sydney College) Modeling a Linear Relationship Wed, Nov 9, 2011 5 / 49Bivariate DataDefinition (Bivariate)Data are called bivariate if two observations, which we will call x and y,are made for each member of the sample.x is the explanatory variable.y is the response variable.x is also called the independent variable.y is also called the dependent variable.Robb T. Koether (Hampden-Sydney College) Modeling a Linear Relationship Wed, Nov 9, 2011 6 / 49ScatterplotsDefinition (Scatterplot)A scatterplot is a display in which each observation (x, y) is plotted asa point in the xy-plane.Open the file Painkillers.xls.See the article Painkiller Overdose Deaths Triple.Make a scatterplot of the data.What does it indicate?What are the unusual values?Robb T. Koether (Hampden-Sydney College) Modeling a Linear Relationship Wed, Nov 9, 2011 7 / 49Free Lunches vs. Graduation RatesExample (Free-lunch Rate vs. Graduation Rate)Is the free-lunch rate in a school district correlated with thegraduation rate in that district?Recently the Richmond Times-Dispatch published data for schooldistricts in the Richmond area.We will draw a scatterplot of the data and see what it looks like.Robb T. Koether (Hampden-Sydney College) Modeling a Linear Relationship Wed, Nov 9, 2011 8 / 49Free Lunches vs. Graduation RatesExample (Free-lunch Rate vs. Graduation Rate)District Free Lunch Grad. Rate District Free Lunch Grad. RateAmelia 41.2 68.9 King and Queen 59.9 64.1Caroline 40.2 62.9 King William 27.9 67.0Charles City 45.8 67.7 Louisa 44.9 80.1Chesterfield 22.5 80.5 New Kent 13.9 77.0Colonial Hgts 25.7 73.0 Petersburg 61.6 54.6Cumberland 55.3 63.9 Powhatan 12.2 89.3Dinwiddie 45.2 71.4 Prince George 30.9 85.0Goochland 23.3 76.3 Richmond 74.0 46.9Hanover 13.7 90.1 Sussex 74.8 59.0Henrico 30.2 81.1 West Point 19.1 82.0Hopewell 63.1 63.4Robb T. Koether (Hampden-Sydney College) Modeling a Linear Relationship Wed, Nov 9, 2011 9 / 49Scatter PlotExample (Free-lunch Rate vs. Graduation Rate)Free Lunch Rate vs. Graduation RateFree Lunch RateGraduation Rate10 20 30 6050400 70 80405060708090Robb T. Koether (Hampden-Sydney College) Modeling a Linear Relationship
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