For the accompanying data
set, (a) draw a scatter diagram of the
data, (b) compute the correlation
(c) determine whether there is a linear relation between x and y.
A student at a junior college conducted a survey of 20 randomly selected full-time students to determine the relation between the number of hours of video game playing each week, x, and grade-point average, y. She found that a linear relation exists between the two variables. The least-squares regression line that describes this relation is ModifyingAbove y with caret equals negative 0.0505 x plus 2.9315y=−0.0505x+2.9315.
(a) Predict the grade-point average of a student who plays video games 8 hours per week.
An author of a book discusses how statistics can be used to judge both a baseball player’s potential and a team’s ability to win games. One aspect of this analysis is that a team’s on-base percentage is the best predictor of winning percentage. The on-base percentage is the proportion of time a player reaches a base. For example, an on-base percentage of 0.3 would mean the player safely reaches bases 3 times out of 10, on average. For a certain baseball season, winning percentage, y, and on-base percentage, x, are linearly related by the least-squares regression equation ModifyingAbove y with caretyequals=2.942.94xnegative 0.4871−0.4871. Complete parts (a) through (d).
(d) A certain team had an on-base percentage of 0.3260.326 and a winning percentage of 0.5480.548. What is the residual for that team? How would you interpret this residual?
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