91Ó°ÊÓ

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 $\stackrel{Áåœ}{y}=10−2x$

(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.

Step by step solution

01

Given information

02

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 $x$

03

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.

Hence, the observation in the lower-right corner of the plot is influential for the least-squares line.

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