Introduction to Statistics for the Social Sciences SBS200, COMM200, GEOG200, PA200, POL200, or SOC200 Lecture Section 001, Spring 2016 Room 150 Harvill Building 9:00 - 9:50 Mondays, Wednesdays & Fridays Welcome

Schedule of readings Study guide for Exam 4 is online Before our fourth and final exam (May 2nd) OpenStax Chapters 1 – 13 (Chapter 12 is emphasized) Plous Chapter 17: Social Influences Chapter 18: Group Judgments and Decisions

Homework On class website: Please complete homework worksheet #25 Regressions Worksheet Due: Monday, April 25th No class on Friday April 22nd

By the end of lecture today 4/20/16 Simple and Multiple Regression Using correlation for predictions r versus r2 Regression uses the predictor variable (independent) to make predictions about the predicted variable (dependent) Coefficient of correlation is name for “r” Coefficient of determination is name for “r2” (remember it is always positive – no direction info) Standard error of the estimate is our measure of the variability of the dots around the regression line (average deviation of each data point from the regression line – like standard deviation) Coefficient of regression will “b” for each variable (like slope)

Sample memorandum and general instructions for Project 4 are both online

Sample memorandum and general instructions for Project 4 are both online

Sample memorandum and general instructions for Project 4 are both online

Starting next week there will be no more Lab sessions Starting next week there will be no more labs this semester

Some useful terms Regression uses the predictor variable (independent) to make predictions about the predicted variable (dependent) Coefficient of correlation is name for “r” Coefficient of determination is name for “r2” (remember it is always positive – no direction info) Standard error of the estimate is our measure of the variability of the dots around the regression line (average deviation of each data point from the regression line – like standard deviation)

Describe relationship Regression line (and equation) r = 0.71 Rory’s Regression: Predicting sales from number of visits (sales calls) Describe relationship Regression line (and equation) r = 0.71 Correlation: This is a strong positive correlation. Sales tend to increase as sales calls increase Predict using regression line (and regression equation) b = 11.579 (slope) Slope: as sales calls increase by 1, sales should increase by 11.579 Dependent Variable Intercept: suggests that we can assume each salesperson will sell at least 20.526 systems a = 20.526 (intercept) Independent Variable Review

Review 50% is explained so the other 50% has yet to be explained (0.71 > 0.632) Review

Summary Intercept: suggests that we can assume each salesperson will sell at least 20.526 systems Slope: as sales calls increase by one, 11.579 more systems should be sold Review

Pop Quiz – First 5 Questions 1. What is regression used for? Include and example 2. What is a residual? How would you find it? 3. What is Standard Error of the Estimate (How is it related to residuals?) 4. Give one fact about r2 5. How is regression line like a mean?

Writing Assignment - 5 Solutions 1. What is regression used for? Include and example Regressions are used to take advantage of relationships between variables described in correlations. We choose a value on the independent variable (on x axis) to predict values for the dependent variable (on y axis).

Writing Assignment - 5 solutions 2. What is a residual? How would you find it? Residuals are the difference between our predicted y (y’) and the actual y data points. Once we choose a value on our independent variable and predict a value for our dependent variable, we look to see how close our prediction was. We are measuring how “wrong” we were, or the amount of “error” for that guess. Y – Y’

Writing Assignment - 5 solutions 3. What is Standard Error of the Estimate (How is it related to residuals?) The average length of the residuals The average error of our guess The average length of the green lines The standard deviation of the regression line

Writing Assignment - 5 solutions 4. Give one fact about r2 It is called a coefficient of determination It is the square of the value for r It is the proportion of variance of the dependent variable that is accounted for by its relationship with the independent variable 5. How is regression line like a mean? The regression line attempts to get as close as possible to the average of the Y values for any particular x score

Thank you! See you next time!!