, Part II David Meredith Department of Mathematics San Francisco State University September 15, 2009
What we will do today 1
Explanatory and Response Variables When you study the relationship between two variables, you usually think of one variable as possible causing or affecting the other.
Explanatory and Response Variables When you study the relationship between two variables, you usually think of one variable as possible causing or affecting the other. The possible cause is called the explanatory variable
Explanatory and Response Variables When you study the relationship between two variables, you usually think of one variable as possible causing or affecting the other. The possible cause is called the explanatory variable The possible effect is called the response variable.
The four cases Explanatory Response Categorical Quantitative Categorical Case II Case I Quantitative Case IV We study only Case I, Case II and.
Representing A situation has a quantitative explanatory variable and a quantitative response variable
Representing A situation has a quantitative explanatory variable and a quantitative response variable How is weight related to height?
Representing A situation has a quantitative explanatory variable and a quantitative response variable How is weight related to height? Graphical representation is a 2d plot
Representing A situation has a quantitative explanatory variable and a quantitative response variable How is weight related to height? Graphical representation is a 2d plot 49ers heights and weights
Textual/Mathematical Representation of A correlation number r that tells how closely the data follow a straight line.
Textual/Mathematical Representation of A correlation number r that tells how closely the data follow a straight line. Correlation between -1 and 1. Closer to -1 or 1, the more the data follows a straight line Positive correlation if data follows a positively sloped line, negative correlation if data follows a negatively sloped line.
Textual/Mathematical Representation of A correlation number r that tells how closely the data follow a straight line. Correlation between -1 and 1. Closer to -1 or 1, the more the data follows a straight line Positive correlation if data follows a positively sloped line, negative correlation if data follows a negatively sloped line. The correlation for the 49ers heights and weights is r = 0.68
Textual/Mathematical Representation of The regression line is the straight line Y = a + bx that best fits the data.
Textual/Mathematical Representation of The regression line is the straight line Y = a + bx that best fits the data. X explanatory values (heights).
Textual/Mathematical Representation of The regression line is the straight line Y = a + bx that best fits the data. X explanatory values (heights). Y response values weights).
Textual/Mathematical Representation of The regression line is the straight line Y = a + bx that best fits the data. X explanatory values (heights). Y response values weights). The line always defined whether the fit is poor or good.
Textual/Mathematical Representation of The regression line is the straight line Y = a + bx that best fits the data. X explanatory values (heights). Y response values weights). The line always defined whether the fit is poor or good.
Equation of Regression Line For the 49ers heights and weights, the regression line is Y = 768.65 + 13.73X
Meaning of slope Slope is 13.73 That means that, on average, each additional inch of height means 13.73 more pounds of weight If one player is 2" taller than another, he will on average weigh 2(13.73)=27.46 pound more If one player is 40 pounds heavier than another, he will on average be 40 = 2.9 inches taller 13.73
Compare two regressions Here are the 49ers Two regressions
Compare two regressions Here are the 49ers Two regressions Slope = 13.7, Correlation = 0.68
Two regressions The Giants
Two regressions The Giants Slope = 3.9, Correlation = 0.37
Two regressions Sometimes we plot two data sets together. (Advanced R)
Two regressions Sometimes we plot two data sets together. (Advanced R)
Two regressions Regression lines highlight the differences in the samples
Two regressions Regression lines highlight the differences in the samples