Chapter 7, Problem 1E

(a)

To determine

To find out which variable you want to use as the explanatory and response variable and why and what would you expect to see in the scatterplot and also discuss the likely direction, form and strength for the same.

Answer to Problem 1E

Weight in grams is the explanatory variable while weight in ounces is the response variable.

There is a positive, linear relationship between the two variables. The relationship is also extremely strong.

Explanation of Solution

Now, we have to find out for the: Apples; weight in grams and weight in ounces.

We know that, the response variable is the focus of a question in a study or experiment. An explanatory variable is one that explains changes in that variable. It can be anything that might affect the response variable.

As we can see that, weight in grams is the explanatory variable and weight in ounces is the response variable because weight in grams is used to predict weight in ounces.

The relationship is positive because as the weight in grams increases, weight in ounces also increases. The relationship is linear because for every increase in one gram, the corresponding weight in ounces increases by the same amount each time. The relationship is extremely long because the relationship between the two variables in completely linear.

(b)

To determine

To find out which variable you want to use as the explanatory and response variable and why and what would you expect to see in the scatterplot and also discuss the likely direction, form and strength for the same

Answer to Problem 1E

Circumference is the explanatory variable while weight is the response variable.

There is a positive, linear relationship between the two variables. The relationship is strong.

Explanation of Solution

Now, we have to find out for the: Apples; circumference (inches) and weight in ounces.

We know that, the response variable is the focus of a question in a study or experiment. An explanatory variable is one that explains changes in that variable. It can be anything that might affect the response variable.

As we can see that,circumference is the explanatory variable and weight is the response variable because circumference is used to predict weight.

The relationship is positive because as circumference increases, weight is also expected to increase. The relationship is linear because for every increase in one inch, there is expected to be a corresponding increase in weight by the same amount each time. The relationship is strong because of the very linear relationship between the two variables.

(c)

To determine

To find out which variable you want to use as the explanatory and response variable and why and what would you expect to see in the scatterplot and also discuss the likely direction, form and strength for the same

Answer to Problem 1E

Shoe size is the explanatory variable and grade point average is the response variable.

There is no direction and form, which means that the strength will be extremely low.

Explanation of Solution

Now, we have to find out for the: College freshmen; shoe size and grade point average.

We know that, the response variable is the focus of a question in a study or experiment. An explanatory variable is one that explains changes in that variable. It can be anything that might affect the response variable.

As we can see that,shoe size is the explanatory variable and GPA is the response variable because shoe size is used to predict GPA.

We cannot predict a direction because there is likely no relationship between the two variables. Therefore, there is no association and the strength of correlation is extremely low.

(d)

To determine

To find out which variable you want to use as the explanatory and response variable and why and what would you expect to see in the scatterplot and also discuss the likely direction, form and strength for the same

Answer to Problem 1E

Number of miles you drove is the explanatory variable and gallons remaining is the response variable.

There is a negative, linear relationship between the variables and the strength is pretty high.

Explanation of Solution

Now, we have to find out for the: Gasoline; number of miles you drove since filling up and gallons remaining in your tank.

We know that, the response variable is the focus of a question in a study or experiment. An explanatory variable is one that explains changes in that variable. It can be anything that might affect the response variable.

As we can see that,number of miles you drove is the explanatory variable and gallons remaining is the response variable because number of miles you drove is used to predict the gallons of gas remaining.

The relationship is negative because as number of miles increases, the number of gallons of gas remaining decreases. The relationship is linear because as the number of miles increases by one, the number of gallons of gas is expected to decrease by the same amount each time. Because of this strong linear relationship, the correlation is high.