Question

read the following description of a data set. the ceo of mcleans natural fruit juice wants to see whether the companys 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 = 0.658x + 23.852. complete the following sentence: 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.

Explanation:

Step1: Recall least - squares regression line formula

The least - squares regression line is given by $y = 0.658x+23.852$, where $x$ is the rating of the first sample and $y$ is the rating of the second sample.

Step2: Analyze the slope

The slope of the regression line is $m = 0.658$. Since $m=0.658> 0$, as $x$ (rating of the first sample) increases, $y$ (rating of the second sample) also increases.

Answer:

The least squares regression line predicts that he or she would rate the second sample 0.658 points higher for every 1 - point higher rating of the first sample.