Scatterplots X and Y Axis Correlation Plots one quantitative variable against another Scatterplots are the best way to start observing the relationship between two quantitative variables Three things to look for in a scatterplot Direction Form Strength Top Left Bottom Right NEGATIVE Bottom Left Top Right POSITIVE Outlier A point that stands away from all others X Axis Independent Variable What is causing the change Y Axis Dependent Variable What is being changed Measures the strength of the linear association between two Tables are compact and give a lot of summary information at a quantitative variables glance Height in inches and height in centimeters have a perfect correlation r 1 Height vs GPA has no correlation o Conditions Quantitative Variables Condition Linearity Condition Outlier Condition o Properties The sign of a correlation coefficient gives the direction of the association Correlation is always between 1 and 1 Correlation treats x and y symmetrically Correlation has no units Correlation is not effected by changes in the center scale of either variable Correlation measures the strength of the linear association between the two variables Correlation is sensitive to unusual observations A third variable which there is always a possibility it may be Lurking Variable affecting both variables Linear Model An equation of a strait line through the data Has two easily estimated parameters a meaningful measure of how well the model fits the data and the ability to predict new values Residual e y y y predicted value y observed value Line of best Fit Line for which the sum of the squared residuals is smallest often called the least squares line AKA Regression Line
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