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Read the following description of a data set. $\newline$ The CEO of McLean's Natural Fruit Juice wants to see whether the company's internal tasters give consistent ratings. He set up a blind taste test in which the tasters rated several samples of fruit juice in the same order, not knowing that two of the samples were actually the same pomegranate-kiwi blend.Each taster rated the samples on a $100$ -point scale. The CEO recorded the ratings that had been given to the first sample of the pomegranate-kiwi blend, $x$ , and the second, $y$ .The least squares regression line of this data set is: $y = 0.659x + 21.481$ $\newline$ Complete the following sentence: $\newline$ For each additional point a taster gave the first sample of the pomegranate-kiwi blend, the least squares regression line predicts that he or she would rate the second sample ___ points higher.

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Interpret regression lines

Full solution

Q. Read the following description of a data set.

\newline

The CEO of McLean's Natural Fruit Juice wants to see whether the company's internal tasters give consistent ratings. He set up a blind taste test in which the tasters rated several samples of fruit juice in the same order, not knowing that two of the samples were actually the same pomegranate-kiwi blend.Each taster rated the samples on a

100

-point scale. The CEO recorded the ratings that had been given to the first sample of the pomegranate-kiwi blend,

x

, and the second,

y

.The least squares regression line of this data set is:

y = 0.659x + 21.481

\newline

Complete the following sentence:

\newline

For each additional point a taster gave the first sample of the pomegranate-kiwi blend, the least squares regression line predicts that he or she would rate the second sample ___ points higher.

Understand regression equation: To solve this problem, we need to understand the equation of the least squares regression line, which is given as $y = 0.659x + 21.481$ . In this equation, ' $x$ ' represents the rating given to the first sample, and ' $y$ ' represents the predicted rating for the second sample.
Interpret coefficient of x: The coefficient of ' $x$ ' in the regression equation represents the slope of the line. This slope tells us how much the predicted value of ' $y$ ' changes for each one-unit increase in ' $x$ '. In this case, the coefficient of ' $x$ ' is $0.659$ .
Predict rating increase: Therefore, for each additional point a taster gave the first sample of the pomegranate-kiwi blend (each one-unit increase in $x$ ), the least squares regression line predicts that the taster would rate the second sample $0.659$ points higher.

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