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Read the following description of a data set. $\newline$ Chandler and Lisa are judges for the Stamford Ice Staking Federation. Due to claims of malfeasance at recent competitions, a reporter is investigating the relationship between the scores awarded by the two judges.She has collected the scores awarded by Chandler, $x$ , and Lisa, $y$ , for each performance in the last competition.The least squares regression line of this data set is: $y = 1.009x + 2.138$ $\newline$ Complete the following sentence: $\newline$ The least squares regression line predicts an increase of $\_\_$ points in the score Lisa awards for an increase of $1$ point in the score Chandler awards.

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Interpret regression lines

Full solution

Q. Read the following description of a data set.

\newline

Chandler and Lisa are judges for the Stamford Ice Staking Federation. Due to claims of malfeasance at recent competitions, a reporter is investigating the relationship between the scores awarded by the two judges.She has collected the scores awarded by Chandler,

x

, and Lisa,

y

, for each performance in the last competition.The least squares regression line of this data set is:

y = 1.009x + 2.138

\newline

Complete the following sentence:

\newline

The least squares regression line predicts an increase of

\_\_

points in the score Lisa awards for an increase of

1

point in the score Chandler awards.

Understand regression line equation: To solve this problem, we need to understand the equation of the least squares regression line, which is given by $y = 1.009x + 2.138$ . In this equation, $y$ represents Lisa's score, and $x$ represents Chandler's score. The coefficient of $x$ ( $1.009$ ) indicates how much $y$ will change for a one-unit change in $x$ .
Interpret coefficient of $x$ : We can interpret the coefficient of $x$ , which is $1.009$ , as the predicted increase in Lisa's score for each additional point awarded by Chandler. This means that for every $1$ point increase in Chandler's score, Lisa's score is predicted to increase by $1.009$ points.

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