2.6 Least-Squares Regression Line Part 2

The mean height of married American women in their early 20s is 64.5 inches and the standard deviation is 2.5 inches. The husbands of these women have a mean height of 68.5 inches, with a standard deviation of 2.7 inches. The correlation between the heights of husbands and wives is about r = 0.5. Find the equation of the least-squares regression line for predicting a husband's height (y variable) from his wife's height (x variable) for married couples in their early 20s.

• $y=33.67+0.54x$

• $y=-0.15+0.29x$

• $y=6.08+1.71x$

• $y=-2.7+0.9x$

Tags

CCSS.HSS.ID.C.8

In professional soccer, it's all about scoring goals. The number of games that a team wins is more strongly correlated with the number of goals the team scores than with the number of goals the team surrenders to its opponent. For the 2013-2014 Premier League in England, the mean number of wins per team was 15.1, with a standard deviation of 6.73. The mean number of goals scored by a team for the entire season was 52.6, with a standard deviation of 20.62. The correlation between these two variables was r = 0.889. Find the equation of the least-squares regression line for predicting the number of wins (y variable) from number of goals scored (x variable).

• $y=33.67+0.54x$

• $y=-0.15+0.29x$

• $y=6.08+1.71x$

• $y=-2.7+0.9x$

Tags

CCSS.HSS.ID.C.8

Some people think that the behavior of the stock market in January predicts its behavior for the rest of the year. Take the explanatory variable x to be the percent change in a stock market index in January and the response variable y to be the change in the index for the entire year. The mean of the percent of change in January is 1.75, and the standard deviation is 5.36. The mean of the change in the index is 9.07, and the standard deviation is 15.35. The correlation between the two is 0.5. Find the equation of the least-squares regression line.

•  $y=33.67+0.54x$  

•  $y=-0.15+0.29x$  

•  $y=6.08+1.71x$  

•  $y=-2.7+0.9x$  

Tags

CCSS.8.EE.C.8C

An ecologist studying breeding habits of a bird called the common crossbill in different years finds that there is a linear relationship between the number of breeding pairs of crossbills and the abundance of spruce cones. In the table, statistics are given for 8 years of measurements, where x = average number of cones per tree and y = number of breeding pairs of crossbills in a certain forest. The correlation is r = 0.968. Find the equation for the least-squares regression line.

•  $y=33.67+0.54x$  

•  $y=-0.15+0.29x$  

•  $y=6.08+1.71x$  

•  $y=-2.7+0.9x$  

Tags

CCSS.8.EE.C.8C