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Unformatted text preview: Chapters 2 and 10: Least Squares Regression Readings: Chapters 2 & 10 1 Introduction Linear Regression : examine association between two quantitative variables. number of beers that you drink and your blood alcohol level homework score and test score Response variable Y : Dependent variable Measures an outcome of a study Explanatory variable X Independent variable Explains or is related to changes in the response variable (p. 105) Example 1 : Which is the explanatory variable and which is the response variable? a. The amount of time spent studying for an exam and the grade on the exam b. The weight in kilograms and the height in centimeters of a person c. Yield of corn in bushels per acre and the inches of rain in the growing season General Procedure for Analyzing Two Quantitative Variables 1. Make a scatter plot of the data. Describe the form, direction, and strength. Look for outliers. 2. Look at the correlation to get a numerical value for the direction and strength. 3. If the data is reasonably linear, get an equation of the line using least squares regression. 4. Look at the residual plot to see if there are any outliers or the possibility of lurking variables. (Patterns bad, randomness good.) 1 5. Look at the normal probability plot to determine whether the residuals are normally distributed. (The dots sticking close to the 45 degree line is good.) 6. Look at hypothesis tests for the correlation, slope, and intercept. Look at confidence intervals for the slope, intercept, and mean response, and at the prediction intervals. 7. If you had an outlier, you should re-work the data without the outlier and comment on the differences in your results. 2 Association Scatter Plot Show the relationship between 2 quantitative variables measured on the same individuals Dots only-dont connect them with a line or a curve Form : Linear? Non-linear? No obvious pattern? Direction : Positive or negative association? No association? Positive association : When above-average values of one variable tend to accom- pany above-average values of the other, and below-average values also tend to occur together. Negative association : When above-average values of one variable tend to accom- pany below average values of the other and visa versa. No association : Hard to find a pattern in the dots Strength : how closely do the points follow a clear form? Strong or weak or moderate? Look for OUTLIERS! Form and direction of an association Linear Non-Linear No Relationship...
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- Spring '08