Question

You take measurements from 550 individuals. You fit the following regression models:

Model 1: Y=a+bx1+cx2+dx3+hx4
​Model 2: Y=a+bx1+cx2+dx3
​Model 3: Y=a+bx1+cx2
​The residual sum of squares for each model is as follows: Model 1: 472 Model 2: 259 Model 3: 312

Answer 1

Residuals from regression models like ý = -173.51 + 4.83x for third exam vs. final exam scores help determine how well the model predicts data. With a significant correlation coefficient (r = 0.6631), this line can be used to predict final exam scores from third exam scores, showing a linear relationship between the variables.

Step-by-step explanation:

The residuals from regression models are key in understanding the accuracy of the models' predictions. When fitting regression models to predict a dependent variable (Y) based on one or more independent variables (x1, x2, x3, etc.), the residual sum of squares (RSS) measures the overall difference between the observed values and the values predicted by the model. In the context provided, you have three regression models with their respective RSS values for predictions involving third exam scores (x) and final exam scores (y).

The goal is to find a line of best fit to accurately predict y, using methods such as the least-squares regression line, which minimizes the sum of the squares of the residuals.

For the third exam vs. final exam example, the least-squares regression line is calculated as ý = -173.51 + 4.83x. Given this line and the correlation coefficient r = 0.6631, we can use it to predict the final exam score based on the third exam score. With a significant r value, which is different from zero, the line can be used for prediction, demonstrating a significant linear relationship between the exam scores.