Chapter 3.1, Problem 9E

(a)

To determine

To make:a scatterplot for the given data

Answer to Problem 9E

  

Explanation of Solution

Given

Speed(km/h)	Fuel used(liters/ $100$ km)	Speed (km/h)	Fuel used(liters/ $100$ km)
$10$	$21.00$	$90$	$7.57$
$20$	$13.00$	$100$	$8.27$
$30$	$10.00$	$110$	$9.03$
$40$	$8.00$	$120$	$9.87$
$50$	$7.00$	$130$	$10.79$
$60$	$5.90$	$140$	$11.77$
$70$	$6.30$	$150$	$12.83$
$80$	$6.95$

Calculation:

We put speed (the explanatory variable) on the horizontal axis and fuel used (the response variable) on the vertical axis, Figure $9.1$ is our completed scatter plot.

  

Conclusion:

Therefore, the required scatterplot is drawn.

(b)

To determine

To describe: the form of the relationship and explain why it is not linear

Answer to Problem 9E

The form of the relationship is slightly curved. Most states fall into one of two distinct clusters

Explanation of Solution

The form of the relationship is slightly curved. It does not mean that two variables are not related but it means that two variables are not linearly related. More important, most states fall into one of two distinct clusters. In about $0$ -speed, the pattern moves from upper left to lower right. That is, states in which lower speed tend to consume more fuel. This is a negative association between the two variables but in next $60-150km/h$ the pattern moves from lower left to upper right. That is, states in which higher speed tend to consume more fuel. This is a positive association between the two variables. It is conclude that if speed is above $60km/h$ fuel consumption increases with speed.

(c)

To determine

To explain: why the variables are not either positively associated or negatively associated

Answer to Problem 9E

Since the relationship is curved not linear, it does not make sense to describe the variables as either positively associated or negatively associated.

Explanation of Solution

Since the relationship is curved not linear, it does not make sense to describe the variables as either positively associated or negatively associated. Positive and negative association works only when variables are linearly related.

(d)

To determine

To explain: whether the relationship is strong or quite weak

Answer to Problem 9E

If data is broke into two parts, then the relationship is very strong If whole data is taken at once and fit it in linear relation then it is weak relationship because overall pattern does not follow a straight line.

Explanation of Solution

If data is broke into two parts, $0-60km/h$ and $60-150km/h$ then the relationship is very strong because in each case pattern follows a straight line. For $0-60km/h$ speed, the pattern moves from upper left to lower right. That is, states in which lower speed tend to consume more fuel. This is a negative association between the two variables but in next $60-150km/h$ the pattern moves from lower left to upper right. That is, states in which higher speed tend to consume more fuel. This isa positive association between the two variables. If whole data is taken at once and fit it in linear relation then it is weak relationship because overall pattern does not follow a straight line.