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Read the following description of a data set. $\newline$ For a project in her statistics class, Diana surveyed her classmates about the extent of their travel experience.Diana asked her classmates how many states, $x$ , and how many countries, $y$ , they had visited.The least squares regression line of this data set is: $y = 1.136x - 3.209$ $\newline$ Complete the following sentence: $\newline$ If a student has visited one additional state, the least squares regression line predicts that he or she would have visited ___ more countries.

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Interpret regression lines

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Q. Read the following description of a data set.

\newline

For a project in her statistics class, Diana surveyed her classmates about the extent of their travel experience.Diana asked her classmates how many states,

x

, and how many countries,

y

, they had visited.The least squares regression line of this data set is:

y = 1.136x - 3.209

\newline

Complete the following sentence:

\newline

If a student has visited one additional state, the least squares regression line predicts that he or she would have visited ___ more countries.

Regression Line Explanation: The least squares regression line provided is $y = 1.136x - 3.209$ . This equation predicts the number of countries, $y$ , a student has visited based on the number of states, $x$ , they have visited.
Coefficient Analysis: To find out how many more countries a student would have visited if they visited one additional state, we need to look at the coefficient of $x$ in the regression equation, which is $1.136$ . This coefficient represents the change in the predicted number of countries for each additional state visited.
Predicted Increase: Since the coefficient of $x$ is $1.136$ , this means that for each additional state visited, the regression line predicts that a student would have visited $1.136$ more countries.

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