1. Ch 5 Relationships Between Quantitative Variables (pg 150) –Will use 3 tools to describe, picture, and quantify 1) scatterplot 2) correlation 3) regression equation – Sec 5.1 Looking for Patterns with Scatterplots (pg 152) Scatterpot- two-dimensional graph of the two variables’ measurements Questions to ask: –Average pattern – straight line? curved line? –Direction of pattern Ex 5.1 Height and Handspan –Data on 167 students -- see slide2 –Fig 5.1 (slide 3) looks like a “linear relationship” and “positive association” Def’n (pg 153 ) –Positive association --- values of 1 variable increases as the values of the other variable increases –Negative association – values of 1 increases while the other decreases –Linear relationship – the pattern seems to approximate a straight line

2. Ex 5.2 Driver Age and Maximum Legibility Distance of Highway Signs –See table 5.2 (pg 154) -- see slide 4 –Figure 5.2 ( slide 5) -- appears linear with negative association Curvilinear Patterns (pg 154 ) –Ex 5.3 Development of Musical Preference »Study of 108 people (ages 16 to 86) who scored 28 songs »-- scored from 1 (disliked a lot) to 10 (liked a lot) »-- adjusted so each persons mean score set = to 0 »Fig 5.3 (slide 6) shows results are a curvilinear relationship Indicating Groups Within Data on Scatterplots pg 155 –Fig 5.4 ( slide 7) shows subgroups (male and female) for Fig 5.1(slide 3) Look for Outliers (pg 156) –Ex 5.4 Heights and Foot Lengths – see slide 8 »Potential “outliers” were actually 3 errors in computer entries

3. –Sec 5.2 Describing Patterns with Regression Line (pg 157) Regression Analysis – relationship between a quantitative response variable and 1 or more explanatory variables –use an equation to predict –simplest is a “straight line” Def’n Regression Line (pg 158 ) –Describes how values of a quantitative response variable (y) are related “ on average” to values of quantitative explanatory variable (x) Ex 5.5 Height and Handspan Regression Line (pg 158) --slide 9 –For a specific x-value, can estimate a corresponding y –value –Using regression equation( discussed on pg 159) »Handspan= -3+ 0.35( Height) or ŷ = -3 + 0.35x »So, when x=60 y= -3 +.35(60) = 18 cm » when x=70 y= -3 +.35 (70) = 21.5 cm – Recall equation of a straight line

4. Statistical Relationship versus Deterministic Relationship (pg160) –Deterministic --- no variation –Statistical -- there is variation from an “average pattern” The Equation of a Regression line (pg 160) – –Ex 5.6 Regression for Driver age and maximum Legibility Distance »Fig 5.7(slide 10) shows regression line for data in Fig 5.2 (pg 154) »Chart on pg 161(slide 11) shows Average Maximum Legibility Distance for 3 selected ages » SPSS tip: Analyze>Regression>Linear Prediction Errors and Residuals (pg 163) –Residual = –Ex 5.7 Prediction Errors for Highway Sign data »Chart on page 163 (slide 12) shows “residuals” or “prediction error” »Fig 5.8 (slide 13) shows graphically the residual for x = 27 Least Squares Criterion (pg 163) –Find the regression line with the smallest “sum of squared errors” –See formulas on pg 164 : – where