Chapter 7, Problem 33E

(a)

To determine

To make a scatterplot for these data.

Explanation of Solution

The information about the horsepower and the highway gas mileage is given in the question. The scatterplot for the same is given as follows:

  

The horsepower is on the horizontal axis and the highway gas mileage is on the vertical axis.

(b)

To determine

To describe direction, strength and form of the plot.

Answer to Problem 33E

Direction is negative, form is linear and the strength is moderately strong.

Explanation of Solution

The information about the horsepower and the highway gas mileage is given in the question. And the scatterplot of the horsepower and the highway gas mileage is in part (a). By this we know that the association between the horsepower and the highway gas mileage is negative, linear and moderately strong since the points form a downward linear trend and the points are neither too clustered nor too scattered.

(c)

To determine

To find the correlation between the horsepower and the miles per gallon.

Answer to Problem 33E

The correlation between the horsepower and the highway gas mileage is $-0.869$ .

Explanation of Solution

The information about the horsepower and the highway gas mileage is given in the question. Then we will calculate the correlation coefficient of horsepower and the highway gas mileage by using the excel. The data is as:

Horsepower	Highway gas mileage
200	32
230	30
200	30
148	32
291	22
300	20
295	21
140	40
166	34
138	36
306	28
300	18
212	25
158	34
150	30

Formula used:

The CORREL function calculates the correlation coefficient between the two data sets in the excel. The syntax is as:

CORREL(array $1$ ,array $2$ )

Calculation:

Now, we will calculate the correlation coefficient using the excel. We will use the above CORREL function for this and we will have,

  $=\text{CORREL}\left(\text{G8:G22,H8:H22}\right)$

And the answer to this will be as:

Correlation coefficient

-0.868682726

So, the correlation between the horsepower and the highway gas mileage is $-0.869$ .

(d)

To determine

To write a few sentences telling what the plot says about fuel economy.

Explanation of Solution

The information about the horsepower and the highway gas mileage is given in the question. And the correlation between the horsepower and the highway gas mileage is $-0.869$ . Now, since the scatterplot has points in a downward trend, it seems that the greater the horsepower the vehicle has, the less fuel efficient the vehicle is. Also if you want to your vehicle to be fuel efficient i.e., greater mileage, you should buy a vehicle with less horsepower.