Modeling a Linear Relationship Lecture 41 Sections 13 1 13 3 1 Robb T Koether Hampden Sydney College Wed Nov 9 2011 Robb T Koether Hampden Sydney College Modeling a Linear Relationship Wed Nov 9 2011 1 49 Outline 1 Introduction 2 Scatterplots 3 Describing Relationships 4 Scatterplots on the TI 83 5 Linear Regression Which Line is Better Measuring the Goodness of Fit 6 Assignment Robb T Koether Hampden Sydney College Modeling a Linear Relationship Wed Nov 9 2011 2 49 Outline 1 Introduction 2 Scatterplots 3 Describing Relationships 4 Scatterplots on the TI 83 5 Linear Regression Which Line is Better Measuring the Goodness of Fit 6 Assignment Robb T Koether Hampden Sydney College Modeling a Linear Relationship Wed Nov 9 2011 3 49 Introduction In Chapter 13 we will investigate the relationship between two quantitative variables Robb T Koether Hampden Sydney College Modeling a Linear Relationship Wed Nov 9 2011 4 49 Introduction In Chapter 13 we will investigate the relationship between two quantitative variables In Chapter 14 we will investigate the relationship between two or more qualitative variables Robb T Koether Hampden Sydney College Modeling a Linear Relationship Wed Nov 9 2011 4 49 Introduction In Chapter 13 we will investigate the relationship between two quantitative variables In Chapter 14 we will investigate the relationship between two or more qualitative variables In Chapter 13 the basic problems will be Robb T Koether Hampden Sydney College Modeling a Linear Relationship Wed Nov 9 2011 4 49 Introduction In Chapter 13 we will investigate the relationship between two quantitative variables In Chapter 14 we will investigate the relationship between two or more qualitative variables In Chapter 13 the basic problems will be Determine whether there is a relationship Robb T Koether Hampden Sydney College Modeling a Linear Relationship Wed Nov 9 2011 4 49 Introduction In Chapter 13 we will investigate the relationship between two quantitative variables In Chapter 14 we will investigate the relationship between two or more qualitative variables In Chapter 13 the basic problems will be Determine whether there is a relationship If there is one then describe it quantitatively Robb T Koether Hampden Sydney College Modeling a Linear Relationship Wed Nov 9 2011 4 49 Introduction In Chapter 13 we will investigate the relationship between two quantitative variables In Chapter 14 we will investigate the relationship between two or more qualitative variables In Chapter 13 the basic problems will be Determine whether there is a relationship If there is one then describe it quantitatively Through this quantitative description we will to be able to predict the 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 49 Outline 1 Introduction 2 Scatterplots 3 Describing Relationships 4 Scatterplots on the TI 83 5 Linear Regression Which Line is Better Measuring the Goodness of Fit 6 Assignment Robb T Koether Hampden Sydney College Modeling a Linear Relationship Wed Nov 9 2011 5 49 Bivariate Data Definition 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 49 Scatterplots Definition Scatterplot A scatterplot is a display in which each observation x y is plotted as a 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 49 Free Lunches vs Graduation Rates Example Free lunch Rate vs Graduation Rate Is the free lunch rate in a school district correlated with the graduation rate in that district Recently the Richmond Times Dispatch published data for school districts 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 49 Free Lunches vs Graduation Rates Example Free lunch Rate vs Graduation Rate District Amelia Caroline Charles City Chesterfield Colonial Hgts Cumberland Dinwiddie Goochland Hanover Henrico Hopewell Free Lunch 41 2 40 2 45 8 22 5 25 7 55 3 45 2 23 3 13 7 30 2 63 1 Robb T Koether Hampden Sydney College Grad Rate 68 9 62 9 67 7 80 5 73 0 63 9 71 4 76 3 90 1 81 1 63 4 District King and Queen King William Louisa New Kent Petersburg Powhatan Prince George Richmond Sussex West Point Modeling a Linear Relationship Free Lunch 59 9 27 9 44 9 13 9 61 6 12 2 30 9 74 0 74 8 19 1 Grad Rate 64 1 67 0 80 1 77 0 54 6 89 3 85 0 46 9 59 0 82 0 Wed Nov 9 2011 9 49 Scatter Plot Example Free lunch Rate vs Graduation Rate Free Lunch Rate vs Graduation Rate Graduation Rate 90 80 70 60 50 40 0 Robb T Koether Hampden Sydney College 10 20 30 40 50 60 Free Lunch Rate Modeling a Linear Relationship 70 80 Wed Nov 9 2011 10 49 Outline 1 Introduction 2 Scatterplots 3 Describing Relationships 4 Scatterplots on the TI 83 5 Linear Regression Which Line is Better Measuring the Goodness of Fit 6 Assignment Robb T Koether Hampden Sydney College Modeling a Linear Relationship Wed Nov 9 2011 11 49 Describing a Relationship Does there appear to be a relationship How can we tell How would we describe the relationship qualitatively and quantitatively Robb T Koether Hampden Sydney College Modeling a Linear Relationship Wed Nov 9 2011 12 49 Linear Association Draw or imagine an oval around the data set If the oval is tilted then there is some linear association If the oval is tilted upwards from left to right then there is positive association If the oval is tilted downwards from left to right then there is negative association If the oval is not tilted at all then there is no association Robb T Koether Hampden Sydney College Modeling a Linear Relationship Wed Nov 9 2011 13 49 Free Lunch Participation vs Graduation Rate Example Free lunch Rate vs Graduation Rate Free Lunch Rate vs Graduation Rate Graduation Rate 90 80 70 60 50 40 0 Robb T Koether Hampden Sydney College 10 20 30 40 50 60 Free Lunch Rate Modeling a Linear Relationship 70 80 Wed Nov 9 2011 14 49 Free Lunch Participation vs Graduation Rate Example Free
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