Data Analysison Regression

Regression: Data Analysis Quick survey Case Studies: 1. Office Trip Study 2. Does an Increasing Crime Rate Decrease House Prices? 3. Analysis of Car Mileage Data

Motivating Examples ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Sales of Houses ,[object Object],[object Object],[object Object],[object Object]

Growth of the economy ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Levels of advertising ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Simple Linear Regression ,[object Object],[object Object],[object Object],[object Object]

Purpose of Modeling ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Forecast Accuracy ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Prediction Interval ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Simple Linear Regression Model ,[object Object],[object Object],[object Object],[object Object]

Simple Linear Regression Model ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Linear Regression ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Best Line ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Least Squares ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Questions ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Discussion on Assumptions ,[object Object],[object Object],[object Object],[object Object],[object Object]

Linear Regression ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Evaluating the Estimated Regression Line ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Reduction of Variability ,[object Object],[object Object],[object Object],[object Object],[object Object]

Analysis of Variance Table ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

The Error SS ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Normal Distribution ,[object Object],[object Object]

How does  determine the dispersion of points about the true regression line? ,[object Object],[object Object]

Assessed Property Values ,[object Object],600 6.00 6.90 LOTSZ 1 0 0 35 10 2.0 5 3 6.00 181.00 1 0 1 32 9 1.0 4 3 11.20 180.00 1 0 1 32 6 1.0 4 3 9.00 165.00 1 0 1 38 7 2.0 3 3 6.00 195.00 0 1 1 35 7 1.0 2 1 6.00 160.00 1 0 1 38 7 1.0 4 3 6.00 159.90 1 0 1 39 6 1.0 3 3 7.00 163.00 0 1 1 35 8 2.0 5 1 6.00 195.00 1 0 0 35 6 2.0 3 3 160.00 0 1 1 30 7 2.0 2 1 215.00 1 0 1 38 8 2 4 3 190.00 LVTTWN EMEADW GARG AGE ROOMS BATH BED RM LOC VALUE

Description of this Data Set ,[object Object],[object Object],[object Object]

Conditional Distributions vs. Marginal Distributions ,[object Object],[object Object]

Plot the conditional distributions for each of these slices ,[object Object],Marginal distribution of price

Key Observations from these Plots: ,[object Object],[object Object],[object Object],[object Object]

Suggestion ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Confirm our intuition by looking at the situation where there is little or no relationship between X and Y . ,[object Object],[object Object]

Compare marginal and conditionals ,[object Object]

Multiple Regression ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

因果關係 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

相關與迴歸 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Office Trip Study ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Scatterplot: AM Trips By Occup. Sq. Ft. (1000) ,[object Object],[object Object]

Residual Plot ,[object Object],[object Object],Noticeable heteroscedasticity by looking at scatter plot. undesirable histogram of residuals

Transformation Attempt #1 ,[object Object],[object Object],[object Object],[object Object],Linear Fit: Log Trips = 1.958 + 0.00208 Occup. Sq. Ft. (1000) Summary of Fit: R 2 = 0.761

New analysis introduces a new problem! ,[object Object],[object Object],[object Object],[object Object],Residual Plot Linear Fit: log Trips = 0.639 + 0.803 log(OccSqFt) Summary of Fit: R 2 = 0.827

Standard Assumptions ,[object Object]

Prediction ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Comparison of the two analyses on a single plot

Does an Increasing Crime Rate Decrease House Prices? ,[object Object],[object Object],[object Object],[object Object],[object Object]

Least squares straight line fit to this data Linear Fit Hs Prc ($10,000) = 22.53 – 0.229 Crime Rate Summary of Fit R 2 = 0.184 R 2 Adj = 0.176 Root Mean Square Error = 7.886 Observations=98

Linear Fit Number (1) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Linear Fit Number (2) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Normal Quantile Plot Normal Quantile Plot Residuals Hs Prc ($10,000); Analysis 1 Residuals Hs Prc ($10,000); Analysis 2

Analysis of Car Mileage Data ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Log(Weight) version provides a somewhat better fit. A slight curve is evident in the residual plot (and in the original scatter plot if you look carefully). No outliers or influential points that seem to warrant special attention.

Another Fit ,[object Object],[object Object],[object Object],--- Linear Fit --- Transformed Fit to Log This suggests that we might want to try also transforming the Y-variable somehow, in order to remove the remaining curved pattern.

Step 1b: Try transformations of Y ,[object Object],[object Object],[object Object],[object Object],R 2 = 0.774344 RMSE = 4.151475 R 2 = 0.705884 RMSE = 4.739567

Transformation ,[object Object],[object Object],[object Object],[object Object],Log 10 (MPG) = 4.2147744 - 0.8388428 Log 10 (Wt)

Transformation ,[object Object],[object Object],[object Object],[object Object]

Step 2: Choose predictor variables for the Multiple Regression ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Plots Actual by Predicted Plot Residual by Predicted Plot

Data Analysison Regression

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