Chapter 3: Q T3.2. (page 200)

The British government conducts regular surveys of household spending. The average weekly household spending (in pounds) on tobacco products and alcoholic beverages for each of $11$ regions in Great Britain was re- corded. A scatterplot of spending on alcohol versus spending on tobacco is shown below. Which of the following statements is true?
(a) The observation $(4.5, 6.0)$ is an outlier.
(b) There is clear evidence of a negative association between spending on alcohol and tobacco.
(c) The equation of the least-squares line for this plot would be approximately $\overset{⏜}{y} = 10 - 2 x$
(d) The correlation for these data is $r = 0.99$
(e) The observation in the lower-right corner of the plot is influential for the least-squares line.

Short Answer

Expert verified

The correct option is (c) The equation of the least-squares line for this plot

would be approximately $\overset{⏜}{y} = 10 - 2 x$

Step by step solution

Given information

Concept

A regression line is a straight line that depicts the relationship between an explanatory variable $x$ and a response variable $y$ By entering any value of $x$ into the equation of the line, you may use a regression line to anticipate the value of $y$ for any value of $x$

Explanation

The following graph depicts a scatterplot of alcohol spending versus tobacco spending. A point with no other points near it that is extreme in the $X$ direction (rounded in the illustration) pulls the line towards itself. Such points are referred to as influential.