Question

A regression line is the line that best fits the data, but this does not mean that the fit is good. In other words, there can still be a lot of variability about the regression line. Which combination describes a regression line that is a good fit for the data?
a. Larger-sq and small Se

b. Larger-sq and large Se

c. Small r-sq and small Se

d. Smallr-sq and large Se

Answer 1

Answer:

The following combination describes a regression line that is a good fit for the data

a. Larger R-sq and small Se

Step-by-step explanation:

In regression analysis, we measure the goodness of fit in terms of two parameters.

1. R² ( R-squared or also called the coefficient of determination)

2. SE ( Standard Error)

1. R-squared

The R-squared indicates the relative measure of the percentage of the variance with respect to the dependent variable.

R-squared is measured in percentage so it doesn't have any unit.

The greater the R-squared percentage, the better is the goodness of fit.

2. Standard Error

The SE basically indicates that on average how far the data points are from the regression line.

The unit of the standard error is the same as the dependent variable.

The lower the SE, the better is the goodness of fit.

Therefore, the correct option is (a)

a. Larger R-sq and small Se