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Title: UCSF - Simple Linear Regression

Lead Author(s): David Glidden, PhD

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Slide 1: Simple Linear Regression

Example Scatterplot

Slide 2: Why regression?

Scatterplot: Mean & 95% CI

Slide 3: Grouping Approach

Scatterplot - Waist Circumference

Slide 4: Linear Regression

Linear Regression (See also: Linear Regression)

Slide 5: Linear Regression Mean

Is Line Reasonable?

Slide 6: Example

Does line fit well?

Slide 7: Scatterplot Smoother

Scatterplot with line

Slide 8: Suppose - Let's consider 4 equal-sized groups

Slide 9: Scatterplot Smoother

Slide 10: STATA

Linear regression variability

Slide 11: Next Example

Slide 12: Scatterplot + Fitted

Scatterplot and Fitted

Slide 13: Least Squares

Simple Linear Regression - Scatterplot
(See also: Least Squares)

Slide 14: Effect of Outlier

Which fits better?

Slide 15: Interpreting Regression

Less influence of outlier

Slide 16: Intercept/Slope

Intercept and Slope

Slide 17: Questions a Regression Can Answer

Questions a regression can answer

Slide 18: Answers - Question 1

Question 1: How does mean HDL vary with waist circumference?

Question 1 Answer

Slide 19: Answers - Question 2

Question 2: Is the association significant?

Question 2 Answer

Slide 20: Answers - Question 3

Question 3: How much of HDL variation is explained by variation in waist circumference?

Question 3 Answer

Slide 21: Answers - Question 3

Question 3

Slide 22: Sample Paragraph

There is an inverse association between waist circumference and HDL (p=0.002) with each one cm increase in waist circumference associated with a -0.196 mg/dL decrease in HDL, 95% CI (-0.32,-0.07). Even though the relationship was significant, waist circumference accounted for only 4% of the observed variance in HDL.

Slide 23: Good Paragraph

Slide 24: Confounding

(See also: Bias or Confounding)

Slide 25: Summary