PCA or Factor Analysis

• Use any data set having continuous variables and perform PCA or Factor Analysis on SAS
• Interpret the results using the methods:

  1.Backward Elimination

  2.Forward Selection

  3.Stepwise Regression

Question: Is the data be more efficiently expressed using PCA? How big are the 1^st, 2^nd, and 3^rd components? Consideration is made for using interesting data and insights. Use literature and SAS for the pointer on interpretation.

Factor Analysis Results The FACTOR Procedure 426 Input Data Type Raw Data Number of Records Read 428 Number of Records Used 426 N for Significance Tests Generated by the SAS System ('Local', X64_10HOME) on July 30, 2020 at 11:33:40 PM Page Break Factor Analysis Results The FACTOR Procedure Initial Factor Method: Principal Components Prior Communality Estimates: ONE Eigenvalues of the Correlation Matrix: Total = 8 Average = 1 Eigenvalue Difference Proportion Cumulative 1 5.72497581 4.65481819 0.7156 0.7156 2 1.07015763 0.47487554 0.1338 0.8494 3 0.59528208 0.37823426 0.0744 0.9238 4 0.21704782 0.04009292 0.0271 0.9509 5 0.17695490 0.08474294 0.0221 0.9731 6 0.09221196 0.01025963 0.0115 0.9846 7 0.08195233 0.04053487 0.0102 0.9948 8 0.04141746 0.0052 1.0000 2 factors will be retained by the MINEIGEN criterion. Factor Pattern Factor1 Factor2 Engine Size 0.92606 -0.09236 Cylinders 0.88069 -0.19670 Horsepower 0.79326 -0.40981 MPG_City -0.85895 0.25257 MPG_Highway -0.86111 0.24462 Weight 0.91465 0.11374 Wheelbase 0.76811 0.59471 Length 0.74610 0.60395 Variance Explained by Each Factor Factor 1 Factor2 5.7249758 1.0701576 Final Communality Estimates: Total = 6.795133 Engine Size Cylinders Horsepower MPG_City MPG_Highway Weight Wheelbase Length 0.86610943 0.81430489 0.79719624 0.80157952 0.80134621 0.84951575 0.94366708 0.92141432 Generated by the SAS System ('Local', X64_10HOME) on July 30, 2020 at 11:33:40 PM Factor Analysis Results The FACTOR Procedure 426 Input Data Type Raw Data Number of Records Read 428 Number of Records Used 426 N for Significance Tests Generated by the SAS System ('Local', X64_10HOME) on July 30, 2020 at 11:33:40 PM Page Break Factor Analysis Results The FACTOR Procedure Initial Factor Method: Principal Components Prior Communality Estimates: ONE Eigenvalues of the Correlation Matrix: Total = 8 Average = 1 Eigenvalue Difference Proportion Cumulative 1 5.72497581 4.65481819 0.7156 0.7156 2 1.07015763 0.47487554 0.1338 0.8494 3 0.59528208 0.37823426 0.0744 0.9238 4 0.21704782 0.04009292 0.0271 0.9509 5 0.17695490 0.08474294 0.0221 0.9731 6 0.09221196 0.01025963 0.0115 0.9846 7 0.08195233 0.04053487 0.0102 0.9948 8 0.04141746 0.0052 1.0000 2 factors will be retained by the MINEIGEN criterion. Factor Pattern Factor1 Factor2 Engine Size 0.92606 -0.09236 Cylinders 0.88069 -0.19670 Horsepower 0.79326 -0.40981 MPG_City -0.85895 0.25257 MPG_Highway -0.86111 0.24462 Weight 0.91465 0.11374 Wheelbase 0.76811 0.59471 Length 0.74610 0.60395 Variance Explained by Each Factor Factor 1 Factor2 5.7249758 1.0701576 Final Communality Estimates: Total = 6.795133 Engine Size Cylinders Horsepower MPG_City MPG_Highway Weight Wheelbase Length 0.86610943 0.81430489 0.79719624 0.80157952 0.80134621 0.84951575 0.94366708 0.92141432 Generated by the SAS System ('Local', X64_10HOME) on July 30, 2020 at 11:33:40 PM