Introduction to Statistics for the Social Sciences SBS200 - Lecture Section 001, Spring 2018 Room 150 Harvill Building 9:00 - 9:50 Mondays, Wednesdays & Fridays. Welcome 4/11/18

Lecturer’s desk Projection Booth Screen Screen Harvill 150 renumbered Row A 15 14 Row A 13 12 11 10 9 8 7 6 5 4 3 2 1 Row A Row B 23 22 21 20 Row B 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row B Row C 25 24 23 22 21 Row C 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row C Row D 29 28 27 26 25 24 23 Row D 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row D Row E 31 30 29 28 27 26 25 24 23 Row E 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row E Row F 35 34 33 32 31 30 29 28 27 26 Row F 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row F Row G 35 34 33 32 31 30 29 28 27 26 Row G 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row G Row H 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 Row H 12 11 10 9 8 7 6 5 4 3 2 1 Row H 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 Row J 13 12 11 10 9 8 7 6 5 4 3 2 1 Row J 41 40 39 38 37 36 35 34 33 32 31 30 29 Row K 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row K Row L 33 32 31 30 29 28 27 26 25 Row L 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row L Row M 21 20 19 Row M 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row M Row N 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row P 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Harvill 150 renumbered table 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Projection Booth Left handed desk

Schedule of readings Before our fourth and final exam (April 30th) OpenStax Chapters 1 – 13 (Chapter 12 is emphasized) Plous Chapter 17: Social Influences Chapter 18: Group Judgments and Decisions

Lab sessions Project 4 This week

Project 4 - Two Correlations - Two Regression Analyses This lab builds on the work we did in our very first lab. But now we are using the correlation for prediction. This is called regression analysis Project 4 - Two Correlations - Two Regression Analyses

Correlation matrices We want to predict home price - What do we care about? We measured the following characteristics of 150 homes recently sold Price Square Feet Number of Bathrooms Lot Size Median Income of Buyers

Correlation matrices What do we care about?

Correlation matrices What do we care about?

Correlation matrices What do we care about?

α = .05 Critical r value from table df = 148 pairs Critical value r(148) = 0.195 df = # pairs - 2

Correlation matrices What do we care about? Critical value from table r(148) = 0.195

+0.9199 3 0.878

+0.9199 3 0.878 Yes Yes The relationship between the hours worked and weekly pay is a strong positive correlation. This correlation is significant, r(3) = 0.92; p < 0.05

3 -0.73 3 0.878 No No The relationship between wait time and number of operators working is negative and strong, but not reliable enough to reach significance. This correlation is not significant, r(3) = -0.73; n.s.

We are measuring 9 students

Critical r = 0.666 4.0 3.0 2.0 1.0 4.0 3.0 2.0 1.0 4.0 3.0 2.0 1.0 GPA GPA GPA 0 1 2 3 4 0 200 300 400 500 600 0 200 300 400 500 600 High School GPA SAT (Verbal) SAT (Mathematical) Do not reject null r is not significant Do not reject null r is not significant Reject Null r is significant r(7) = 0.50 r(7) = + 0.80 r(7) = + 0.80 r(7) = + 0.911444123 r(7) = + 0.616334867 r(7) = + 0.487295007

4.0 3.0 2.0 1.0 4.0 3.0 2.0 1.0 4.0 3.0 2.0 1.0 GPA GPA GPA 0 1 2 3 4 0 200 300 400 500 600 0 200 300 400 500 600 High School GPA SAT (Verbal) SAT (Mathematical) r(7) = 0.50 r(7) = + 0.80 r(7) = + 0.80 r(7) = + 0.911444123 r(7) = + 0.616334867 r(7) = + 0.487295007

4.0 3.0 2.0 1.0 4.0 3.0 2.0 1.0 4.0 3.0 2.0 1.0 GPA GPA GPA 0 1 2 3 4 0 200 300 400 500 600 0 200 300 400 500 600 High School GPA SAT (Verbal) SAT (Mathematical) r(7) = 0.50 r(7) = + 0.80 r(7) = + 0.80 r(7) = + 0.911444123 r(7) = + 0.616334867 r(7) = + 0.487295007

4.0 3.0 2.0 1.0 4.0 3.0 2.0 1.0 4.0 3.0 2.0 1.0 GPA GPA GPA 0 1 2 3 4 0 200 300 400 500 600 0 200 300 400 500 600 High School GPA SAT (Verbal) SAT (Mathematical) r(7) = 0.50 r(7) = + 0.80 r(7) = + 0.80 r(7) = + 0.911444123 r(7) = + 0.616334867 r(7) = + 0.487295007

Correlation: Independent and dependent variables When used for prediction we refer to the predicted variable as the dependent variable and the predictor variable as the independent variable What are we predicting? What are we predicting? Dependent Variable Dependent Variable Independent Variable Independent Variable

Correlation - What do we need to define a line If you probably make this much Expenses per year Yearly Income Y-intercept = “a” (also “b0”) Where the line crosses the Y axis Slope = “b” (also “b1”) How steep the line is If you spend this much The predicted variable goes on the “Y” axis and is called the dependent variable The predictor variable goes on the “X” axis and is called the independent variable

Dustin spends $12 for his Birthday Angelina Jolie Buys Brad Pitt a $24 million Heart-Shaped Island for his 50th Birthday Angelina probably makes this much Expenses per year Yearly Income Dustin probably makes this much Dustin spent this much Angelina spent this much Dustin spends $12 for his Birthday Revisit this slide

Assumptions Underlying Linear Regression For each value of X, there is a group of Y values These Y values are normally distributed. The means of these normal distributions of Y values all lie on the straight line of regression. The standard deviations of these normal distributions are equal. Revisit this slide

Correlation - the prediction line - what is it good for? Prediction line makes the relationship easier to see (even if specific observations - dots - are removed) identifies the center of the cluster of (paired) observations identifies the central tendency of the relationship (kind of like a mean) can be used for prediction should be drawn to provide a “best fit” for the data should be drawn to provide maximum predictive power for the data should be drawn to provide minimum predictive error

Predicting Restaurant Bill Prediction line Y’ = a + b1X1 Cost will be about 95.06 Predicting Restaurant Bill Cost Y-intercept The expected cost for dinner for two couples (4 people) would be $95.06 Cost = 15.22 + 19.96 Persons People If People = 4 Slope If “Persons” = 4, what is the prediction for “Cost”? Cost = 15.22 + 19.96 Persons Cost = 15.22 + 19.96 (4) Cost = 15.22 + 79.84 = 95.06 If “Persons” = 1, what is the prediction for “Cost”? Cost = 15.22 + 19.96 Persons Cost = 15.22 + 19.96 (1) Cost = 15.22 + 19.96 = 35.18

Rent = 150 + 1.05 SqFt Rent = 150 + 1.05 (800) Rent = 150 + 840 = 990 Prediction line Y’ = a + b1X1 Rent will be about 990 Predicting Rent Cost Y-intercept Slope If SqFt = 800 Square Feet The expected cost for rent on an 800 square foot apartment is $990 Rent = 150 + 1.05 SqFt If “SqFt” = 800, what is the prediction for “Rent”? Rent = 150 + 1.05 SqFt Rent = 150 + 1.05 (800) Rent = 150 + 840 = 990 If “SqFt” = 2500, what is the prediction for “Rent”? Rent = 150 + 1.05 SqFt Rent = 150 + 1.05 (2500) Rent = 150 + 2625 = 2,775

Thank you! See you next time!!