Question

Demand for Soft Drinks A convenience store manager notices that sales of soft drinks are higher on hotter days, so he assembles the data in the table.

(a) Make a scatter plot of the data.

(b) Find and graph a linear function that models the data.

(c) Use the model to predict soft drink sales if the temperature is ${95}^o$F.

Short answer

(a) The scatter plot is

(b) The regression line equation is$y=16.4x-621$ and the graph is,

(c) 937 cans were sold when the temperature is ${95}^{\circ }$F.

Step-by-step solution

Part a. Step 1. Concept of plotting the data.

Among the given variables we assign one of them is abscissa and the other at ordinate. Thus, we get some coordinates,

To get the scatter plot we plot the point.

Part a. Step 2. Assumption of variables.

Let us assign the temperature at abscissa and number of cans sold at ordinate.

Part a. Step 3. Plotting the graph.

The given table is,

So, the scatter plot is,

Part b. Step 1. Concept of regression line.

A regression line is a simple line that best fits the data.

Part b. Step 2. Given conditions.

The given table is,

So, the scatter plot is,

Part b. Step 3. Find the equation of line.

By using graphing ability, the equation of regression line here is $y=16.4x-621$.

Part c. Step 1. Concept of finding of variables.

The value of one is known and the other is not. Then we substitute the known value in the equation. So, we get the value of the other variable.

Part c. Step 2. Given conditions.

Since, the regression line equation for temperature and number of cans sold is $y=16.4x-621$.

We have to find the number of cans sold when temperature is ${95}^{\circ }$F.

Part c. Step 3. Finding the value.

When $x={95}^{\circ }$F.

Then$$\begin{gathered} y=16.4\times 95-621 \\ =937. \end{gathered}$$