Question

Complete the sentence: the best-fitting regression line can be used to _____.

a. find the actual value of the dependent variable for a given independent variable
b. estimate or predict the value of the dependent variable for a given independent variable
c. calculate the correlation coefficient
d. all of the above
e. none of the above

Answer 1

b. estimate or predict the value of the dependent variable for a given independent variable

Explanation:

In statistics linear regression is a mathematical model used to approximate the dependency relationship between a dependent variable
`Y`, and one or more independent variables
`(X_1,X_2,...X_i)`, and a random term
`\varepsilon`. In the simplest case, with a single explicit variable, this is simply a straight line:

`Y=\beta_o + \beta_1 X`

Where
`\beta_o` and
`\beta_1` are parameters that define the position and inclination of the line.

Answer 2

The regression line provides an estimate of the dependent value. It can only predict the actual value if the correlation coefficient is ±1. The most appropriate choice is ...

... b. estimate or predict the value of the dependent variable for a given independent variable