Question

C. Interaction Test (8 points) - Fill in the following information for your test. Full Model: Reduced Model: Test: Ho: Ha: Test Statistic: P-value: Conclusion: Least Squares Linear Regression of Rent Predictor Variables Constant Size Location X1X2 Coefficient 1532.52 -0.17545 -332.138 0.49286 Std Error 658.456 0.62872 931.704 0.85707 T 2.33 -0.28 -0.36 0.58 P 0.0244 0.7814 0.7231 0.5681 VIF 0.0 2.2 23.3 26.3 Mean Square Error (MSE) Standard Deviation 465466 682.251 R2 Adjusted R AIS DPRESS 0.0303 -0.0329 659.73 2.41E+07 F 0.48 Source Regression Residual Total Р 0.6981 DF 3 46 49 MS 223225 465 466 SS 669676 2.141E+07 2.208E+07 M M Lack of Fit Pure Error 44 2 2.141E+07 0.00000 486624 0.00000 Cases Included 50 Missing Cases 0 6. Would your model building be finished after the interaction test of question 5? Why or why not? (2 points)

Answer 1

Full Model: E(y) = β₀ + β₁x₁ + β₂x₁² + β₃x₂ + β₄x₁x₂ + β₅x₁²x₂

Reduced Model: E(y) = β₀ + β₁x₁ + β₂x₂ + β₃x₁x₂

The hypothesis being tested is:

H₀: β₁ = β₂ = β₃ = 0

H₁: At least one β_i ≠ 0

F = 0.48

The p-value is 0.6981.

Since the p-value (0.6981) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we cannot conclude that the model is significant.