Question

Homework #4

Prediction & Model Evaluation

                                                                       X                                       Y

                                                                   2.13                                 16.82

                                                                   1.62                                 10.06

                                                                   2.80                                 28.68

                                                                   1.36                                  7.78

                                                                   1.41                                  7.70

                                                                   0.53                                  1.91

                                                                   1.23                                  6.48

                                                                   1.99                                 14.94

                                                                   3.75                                 50.13

                                                                   2.09                                 16.19

                                                                   1.61                                 10.33

1. Assume that a linear model might capture the relationship between these variables. Estimate the parameters of a linear model for these data. Here are a few building blocks to help you: M_x = 1.87, SD_x = 0.86;; M_y = 15.55, SD_y = 12.86;; r_xy = 0.97.   

2. Given the parameters you calculated for this model, how well does the model capture the data (i.e. Calculate R²)?

3. Visually display what R² reveals concerning the relationship between the variables X

& Y?     

4. Imagine someone else proposed an alternative model with the form: Y = a + bX², with a = 0.2 and b = 3.5. Which of these models (the one proposed here or the one proposed in question one) best describes the data? How do you know this?

5. What is considered the worst fitting model possible?    What would be the error variance for this model?

Answer 1