Question

suppose we fit the least-squares regression line to a set of data. the plot of the residuals is given below. plot of residuals this plot suggests that select one: a. the correlation must be 0. b. outliers must be present. c. the linear least-squares regression line is not appropriate for the data. d. the linear least-squares regression line is appropriate for the data since the residuals are small.

Answer 1

The right option is c, The linear least-squares regression line is not appropriate for the data. A straight line is not an effective way to summarize the data.

A least-squares regression line, which minimizes the vertical distance between the data points and the regression line, is the line that best fits a linear connection between two variables when the data indicates such a relationship.

Given that the terms "linear least squares" and "linear regression" relate to two distinct concepts, we should differentiate between them. The former refers to fitting a model that is a linear function of the independent variable, and the latter refers to fitting a model that is linear in the parameters.

To understand more about least-squares regression, have a look at this example:

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The right question is:

Suppose we fit the least-squares regression line to a set of data. If a plot of the residuals shows a curved pattern,

A. a straight line is not a good summary of the data.

B. the correlation must be 0.

C. the correlation must be positive.

D. outliers must be present.

E. r2 = 0.