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

On class website: Please complete homework worksheet #24 Please complete the homework modules on the D2L website Hypothesis Testing, Correlations Due: Friday, April 15 th Homework Please note: In the graded quiz portion of the online D2L Homework 24 you will be asked to access Zeanna's data. The link within the homework may not work properly. Please download the Excel file on the class website or within D2L to complete the homework assignment

By the end of lecture today 4/13/16 Project 4 Simple Regression Using correlation for predictions

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

Labs will meet this week Project 4

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

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. 3

We are measuring 9 students

High School GPA GPA r(7) = 0.50 r(7) = SAT (Verbal) GPA r(7) = r(7) = SAT (Mathematical) GPA r(7) = r(7) = Critical r = Reject Null r is significant Do not reject null r is not significant Do not reject null r is not significant

High School GPA GPA r(7) = 0.50 r(7) = SAT (Verbal) GPA r(7) = r(7) = SAT (Mathematical) GPA r(7) = r(7) =

High School GPA GPA r(7) = 0.50 r(7) = SAT (Verbal) GPA r(7) = r(7) = SAT (Mathematical) GPA r(7) = r(7) =

High School GPA GPA r(7) = 0.50 r(7) = SAT (Verbal) GPA r(7) = r(7) = SAT (Mathematical) GPA r(7) = r(7) =

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 Dependent Variable Dependent Variable Independent Variable Independent Variable What are we predicting?

Correlation - What do we need to define a line Expenses per year Yearly Income Y-intercept = “a” ( also “b 0 ”) Where the line crosses the Y axis Slope = “b” ( also “b 1 ”) How steep the line is If you spend this much If you probably make 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

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

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

Correlation - the prediction line 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 - what is it good for?

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

Predicting Rent The expected cost for rent on an 800 square foot apartment is $990 Rent = SqFt If “SqFt” = 800, what is the prediction for “Rent”? Rent = SqFt Rent = (800) Rent = = 990 Prediction line Y’ = a + b 1 X 1 Y-intercept Slope Square Feet Cost If SqFt = 800 Rent will be about 990 If “SqFt” = 2500, what is the prediction for “Rent”? Rent = SqFt Rent = (2500) Rent = = 2,775