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Introduction to Statistics for the Social Sciences SBS200 - Lecture Section 001, Spring 2019 Room 150 Harvill Building 9:00 - 9:50 Mondays, Wednesdays & Fridays. April 15
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The Green Sheets
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Schedule of readings Before our fourth and final exam (April 29th)
OpenStax Chapters 1 – 13 (Chapter 12 is emphasized) Plous Chapter 17: Social Influences Chapter 18: Group Judgments and Decisions
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Labs continue this week
Lab sessions Labs continue this week
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Project 4 - Two Correlations - Two Regression Analyses
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Homework Due Date Extended
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regression coefficient
We refer to the predicted variable as the dependent variable (Y) and the predictor variable (X) as the independent variable Why are we finding the regression line? How would we use it? regression coefficient (slope) correlation coefficient (“r”)
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Regression Example Rory is an owner of a small software company and employs 10 sales staff. Rory send his staff all over the world consulting, selling and setting up his system. He wants to evaluate his staff in terms of who are the most (and least) productive sales people and also whether more sales calls actually result in more systems being sold. So, he simply measures the number of sales calls made by each sales person and how many systems they successfully sold.
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Do more sales calls result in more sales made?
Regression Example 60 70 Number of sales calls made systems sold 10 20 30 40 50 Ava Emily Do more sales calls result in more sales made? Isabella Emma Step 1: Draw scatterplot Ethan Step 2: Estimate r Joshua Jacob Dependent Variable Independent Variable
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Regression Example Do more sales calls result in more sales made? Step 3: Calculate r Step 4: Is it a significant correlation?
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Do more sales calls result in more sales made?
Step 4: Is it a significant correlation? n = 10, df = 8 alpha = .05 Observed r is larger than critical r (0.71 > 0.632) therefore we reject the null hypothesis. Yes it is a significant correlation r (8) = 0.71; p < 0.05 Step 3: Calculate r Step 4: Is it a significant correlation?
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Regression: Predicting sales
Step 1: Draw prediction line r = 0.71 b = (slope) a = (intercept) Draw a regression line and regression equation What are we predicting?
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Regression: Predicting sales
Step 1: Draw prediction line r = 0.71 b = (slope) a = (intercept) Draw a regression line and regression equation
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Regression: Predicting sales
Step 1: Draw prediction line r = 0.71 b = (slope) a = (intercept) Draw a regression line and regression equation
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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 = (slope) Slope: as sales calls increase by 1, sales should increase by Dependent Variable Intercept: suggests that we can assume each salesperson will sell at least systems a = (intercept) Independent Variable
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Regression: Predicting sales
You should sell systems Step 1: Predict sales for a certain number of sales calls Madison Step 2: State the regression equation Y’ = a + bx Y’ = x Joshua If make one sales call Step 3: Solve for some value of Y’ Y’ = (1) Y’ = What should you expect from a salesperson who makes 1 calls? They should sell systems If they sell more over performing If they sell fewer underperforming
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Regression: Predicting sales
You should sell systems Step 1: Predict sales for a certain number of sales calls Isabella Step 2: State the regression equation Y’ = a + bx Y’ = x Jacob If make two sales call Step 3: Solve for some value of Y’ Y’ = (2) Y’ = What should you expect from a salesperson who makes 2 calls? They should sell systems If they sell more over performing If they sell fewer underperforming
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Regression: Predicting sales
You should sell systems Ava Step 1: Predict sales for a certain number of sales calls Emma Step 2: State the regression equation Y’ = a + bx Y’ = x If make three sales call Step 3: Solve for some value of Y’ Y’ = (3) Y’ = What should you expect from a salesperson who makes 3 calls? They should sell systems If they sell more over performing If they sell fewer underperforming
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Regression: Predicting sales
You should sell systems Step 1: Predict sales for a certain number of sales calls Emily Step 2: State the regression equation Y’ = a + bx Y’ = x If make four sales calls Step 3: Solve for some value of Y’ Y’ = (4) Y’ = What should you expect from a salesperson who makes 4 calls? They should sell systems If they sell more over performing If they sell fewer underperforming
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Regression: Evaluating Staff
Step 1: Compare expected sales levels to actual sales levels Ava Emma Isabella Emily Madison What should you expect from each salesperson Joshua Jacob They should sell x systems depending on sales calls If they sell more over performing If they sell fewer underperforming
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Regression: Evaluating Staff
Step 1: Compare expected sales levels to actual sales levels =14.7 Difference between expected Y’ and actual Y is called “residual” (it’s a deviation score) Ava 14.7 How did Ava do? Ava sold 14.7 more than expected taking into account how many sales calls she made over performing
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Regression: Evaluating Staff
Step 1: Compare expected sales levels to actual sales levels =-23.7 Difference between expected Y’ and actual Y is called “residual” (it’s a deviation score) Ava -23.7 How did Jacob do? Jacob sold fewer than expected taking into account how many sales calls he made under performing Jacob
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Regression: Evaluating Staff
Step 1: Compare expected sales levels to actual sales levels Ava Emma Isabella Emily Madison What should you expect from each salesperson Joshua Jacob They should sell x systems depending on sales calls If they sell more over performing If they sell fewer underperforming
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Thank you! See you next time!!
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