Chapter 3.1, Problem 4E

(a)

To determine

To find: whether the plot shows a positive or negative association between the variables

Answer to Problem 4E

The plot shows a negative association between the two variables.

Explanation of Solution

Given:

  

The figure below shows a scatterplot of Temperature (degrees Fahrenheit) and Gas consumed (cubic feet). We think that “Tempreature” will help explain “Gas consumed”. So “Tempreature” is the explanatory variable and “Gas consumed” is the response variable. We want to see how Gas consumed changes when Tempreature changes, so we put Tempreature (the explanatory variable) on the horizontal axis and Gas consumed (the response variable) on the vertical axis.

The plot shows a negative association between the two variables.

(b)

To determine

To find:the form of the relationship and explain whether it is very strong.

Answer to Problem 4E

The form of the relationship is linear. The relationship is moderately strong

Explanation of Solution

The form of the relationship is linear. That is, the overall pattern follows a straight line from upper left to lower right. The relationship is moderately strong because the points don’t deviate greatly from line. There are no obvious outliers.

(c)

To determine

To explain:the point at the bottom right of the plot

Answer to Problem 4E

The point $P$ shows that Joan uses $275$ cubic feet gas (approx.) to maintain the temperature $57$ degrees Fahrenheit.

Explanation of Solution

In Figure point $P$ , when perpendicular is drawn from point $P$ to $X$ axis and $Y$ axis, the coordinate of point $P$ is approximately $(57,275)$ . This shows that Joan uses $275$ cubic feet gas (approx.) to maintain the temperature $57$ degrees Fahrenheit.