# Regression Analysis

Explained and unexplained variation and the least-squares regression line

Bivariate data obtained for the paired variables and are shown below, in the table labelled "Sample data." These data are plotted in the scatter plot in Figure 1, which also displays the least-squares regression line for the data. The equation for this line is .

In the "Calculations" table are calculations involving the observed values, the mean of these values, and the values predicted from the regression equation.

1. For the data point (282.4, 268.7) the value of the residual is what? (Round your answer to at least 2 decimal places.

2. Multiple Choice. The least squares regression line is given above is said to be a line which "best fits" the sample data. The term "best fits" is used because the line has an equation that minimizes the

a) total sum of squares

b) regression sum of squares, or

c) error sum of squares,

which for these data is,

a) 5487.2520

b) 837.2700

c) 4671.6604

3. Multiple Choice. The variation in the sample y values that is explained by the estimated linear relationship between x and y is given by

a) total sum of squares

b) regression sum of squares, or

c) error sum of squares

which for these data is,

a) 5487.2520

b) 837.2700

c) 4671.6604

4. The proportion of the total variation in the sample y values that can be explained by the estimated linear relationship between x and y is what? (Round your answer to at least 2 decimal places).

#### Solution Summary

The solution provides step by step method for the calculation of regression model . Formula for the calculation and Interpretations of the results are also included.