Slide 1
Topics
Decisions Based on Relationship Between Two or More Variables
X – Y Data
Regression Analysis
Scatter Chart to “See” If There Is a Relationship
Types of Relationships
Baseball Data Scatter Charts
Slide 9
Scatter Chart and Ybar and X Bar Lines
Covariance
Slide 12
Coefficient of Correlation (rxy)
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Overview: Simple Linear Regression
Simple Liner Regression Model with Population Parameters
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Simple Liner Regression Equation with Population Parameters
Sample Slope and Y-Intercept
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Estimation Process for Simple Linear Regression
Overview: Least Squares Method to Derive Formula for b1 & b0
Formulas for estimated Slope (b1) Y-intercept (b0)
Slide 28
Experimental Region
Slide 30
How to Interpret Slope and Y-Intercept
Prediction with Estimated Simple Liner Regression Equation
Does the Equation Predict Perfectly?
Residuals = Y1 – ŷ = Particular Y value – Predicted Y Value
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How Well Does Estimated Equation/Line Fit the Sample Data?
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Error in Predicting Y Using Equation
Total Error if we used just Ybar
Two Parts in Total Error
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Squaring & then Summing “Total”, “Regression” & “Error”
How to Think About SST and SSE
How to Think About SSR
Relationship Between SST, SSR and SSE
Coefficient of Determination
Slide 50
The Closer to 1, the Better the Fit.
Coefficient of Determination
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Standard Error of the Estimate
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Degrees of Freedom, page 150 in textbook
Data Analysis, Regression feature Step 1: Dialog Box
Data Analysis, Regression feature Step 2: Output
What Regression Output Means
Slide 62
Multiple Regression
Multiple Regression Model & Equation
Estimated Multiple Regression Equation
Coefficient of Determination
Calculating Slope and Y-Intercept for Multiple Regression
Multiple Regression for Credit Card Company Example:
If We Just Tried To Build Equation Based On Annual Income (X1)
Now We Add More Independent Variables
Estimated Multiple Regression Equation For Predicting:
Interpreting Slopes & Intercept in Multiple Regression
Statistical Inference
Inference and Regression
Slide 75
Implication of Assumptions
Visually Testing Assumptions: Plot Residuals Against X Values
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Visually Testing Assumptions: Plot Residuals Against X Values
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If Residual Plots Show Assumptions Are Met:
The Logical Element to Test in Linear Regression: Slope
Hypothesis Test to Check if Slope/s Are Equal to Zero
Steps For Hypothesis Testing
Steps For Hypothesis Testing
Steps For Hypothesis Testing
F Distribution for Hypothesis Test
F Test Statistic for Hypothesis Test
Formulas for testing individual estimates of parameters:
Testing Individual Regression Parameters
t Distribution for Hypothesis Test
Hypothesis Test For Weekly Ad Expense and Sales Example:
Hypothesis Test For Credit Card Example:
What the F Statistic Hypothesis Test Looks Like
Slide 97
Nonsignificant Variables: Reassess Whole Model/Equation
Multicollinearity
Categorical Independent Variables
Categorical Independent Variables
Multiple Regression with Categorical Variable
Slide 103
Inference and Very Large Samples
Small Sample Size