Introduction to Statistics for the Social Sciences SBS200 - Lecture Section 001, Fall 2017 Room 150 Harvill Building 10:00 - 10:50 Mondays, Wednesdays & Fridays. Welcome

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Schedule of readings Before our fourth and final exam (December 4th) OpenStax Chapters 1 – 13 (Chapter 12 is emphasized) Plous Chapter 17: Social Influences Chapter 18: Group Judgments and Decisions

Over next couple of lectures 11/20/17 Logic of hypothesis testing with Correlations Interpreting the Correlations and scatterplots 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)

Lab sessions No Labs this week Everyone will want to be enrolled in one of the lab sessions No Labs this week

No class on Wednesday Happy Holiday!

Homework Assignment

A note on doodling

Project 4 - Two Correlations - We will use these to create two regression analyses

Scatterplot displays relationships between two continuous variables Correlation: Measure of how two variables co-occur and also can be used for prediction Range between -1 and +1 The closer to zero the weaker the relationship and the worse the prediction Positive or negative

by height (centimeters) Positive correlation: as values on one variable go up, so do values for the other variable Negative correlation: as values on one variable go up, the values for the other variable go down Positive Correlation Negative Correlation Perfect Correlation Height of Mothers by height of Daughters Brushing teeth by number cavities Height (inches) by height (centimeters) Height in Centimeters inches Height of Mothers Brushing Teeth Height of Daughters Number Cavities

Correlation - How do numerical values change? Revisit this slide

Final results might look like this Predicting One positive correlation 15 12 9 6 3 “Passion for Gaming” Score Time Studying 0 3 6 9 12 15 20

Regression: Predicting level of passion for gaming Step 1: Draw prediction line b = .7372 (slope) a = 5.72 (intercept) Right click on dots Draw a regression line and regression equation

Regression: Predicting level of passion for gaming Step 1: Draw prediction line b = .7372 (slope) a = 5.72 (intercept) Draw a regression line and regression equation

Regression: Predicting level of passion for gaming Step 1: Draw prediction line b = .7372 (slope) a = 5.72 (intercept) Draw a regression line and regression equation

Regression: Predicting level of passion for gaming Step 1: Draw prediction line b = .7372 (slope) a = 5.72 (intercept) Draw a regression line and regression equation

Regression: Predicting level of passion for gaming Describe relationship Regression line (and equation) r = .67 Correlation: This is a strong positive correlation. Passion tends to increase as number of hours increase Predict using regression line (and regression equation) b = .7372 (slope) Slope: for each additional hour spent studying, passion increase by .7372 points Dependent Variable Intercept: suggests that we can assume each person starts with a baseline passion of 5.72 Independent Variable a = 5.72 (intercept)

Final results might look like this Predicting One positive correlation 80 60 40 20 “Number Systems Sold” Number of Sales Calls 0 3 6 9 12 15 20

Regression: Predicting sales from sales calls Step 1: Draw prediction line Right click on dots Draw a regression line and regression equation

Display Equation and Display R-squared Regression: Predicting sales from sales calls r = 0.7068 b = 11.579(slope) Step 1: Draw prediction line a = 20.526 (intercept) Choose Display Equation and Display R-squared Draw a regression line and regression equation

Regression: Predicting sales from sales calls b = 11.579(slope) Step 1: Draw prediction line a = 20.526 (intercept) Draw a regression line and regression equation

Regression: Predicting sales from sales calls Describe relationship Regression line (and equation) r = 0.7068 Correlation: This is a strong positive correlation. Sales tend to increase as number of sales calls increase Predict using regression line (and regression equation) b = 11.579(slope) Slope: for each additional sales call, sales increase by 11.579. Dependent Variable Intercept: suggests that we can assume each person starts with a baseline sales of 20.526 Independent Variable a = 20.526 (intercept)

How to complete scatterplots, correlations and simple regressions using Excel Real time demo

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

Writing Assignment

Thank you! See you next time!!