Question

A new pizza restaurant uses paid advertisement to increase pizza sales on Mondays. The table below is a record of the restaurant’s sales each Monday for the first quarter (13 weeks) of the paid advertisement.
Week Total Sales
1 $315
2 $376
3 $280
4 $465
5 $399
6 $376
7 $400
8 $422
9 $525
10 $700
11 $410
12 $550
13 $590

Part A: Create a scatter plot to represent the data in the table. Then, draw the line of best fit, going through the points representing weeks 5 and 13. Be sure to label each axis, as well as to include the proper titles for the scatter plot.

Part B: Use the total sales for weeks 5 and 13 to write an equation for the line of best fit. In your final answer, include all of your calculations.

Part C: In terms of the slope of the equation for the lines of best, fit explain whether or not you think the paid advertisement is responsible for the restaurant's increase or decrease in pizza sales during the first quarter. Use complete senteneces in your answer.

Part D: Assuming that the pizza restaurant wishes to continue the paid advertisement for an additional quarter, use the equation for the line of best fit to predict the restaurant's sales for the Monday of the 20th week.

Answer 1

Answer:

Part A:

Find the attached

Part B:

y = 23.875x + 279.625

Part C:

Total Sales increase from one week to the next by $23.875. Therefore, it is true to say that the paid advertisement is responsible for the restaurant's increase in pizza sales during the first quarter.

Part D:

The restaurant's sales for the Monday of the 20th week is expected to be $757.13

Step-by-step explanation:

Part A:

The scatter-plot can be obtained from stat-crunch by following the given steps below;

The first step is to enter the data given into any two adjacent columns of Stat-crunch application.

Next, click on Graph then Scatter plot

In the pop-up window that appears, select the week column as the X variable and the Total Sales column as the Y variable

Click Compute. Stat-crunch returns the scatter-plot as shown in the attachment below.

Part B:

The total sales for week 5 is given as 399 while that of week 13 is 590. Therefore, we shall determine the equation for the line of best fit using the points;

( 5, 399) and ( 13, 590)

The first step would be to determine the slope of this line;

slope = (590 - 399)/ (13 - 5)

         = 23.875

The equation of the line in slope-intercept form is thus;

Sales = 23.875(Week) + c

We need to determine c, the y-intercept. We can use the point ( 5, 399);

399 = 23.875(5) + c

c = 279.625

The equation of the line of best fit is thus;

y = 23.875x + 279.625

Part C:

The slope of the equation for the lines of best fit was found to be 23.875. This value is positive which implies that the Total Sales increase from one week to the next by $23.875. The slope in regression is defined as the change in y for every unit change in x.

Therefore, it is true to say that the paid advertisement is responsible for the restaurant's increase in pizza sales during the first quarter.

Part D:

The equation  for the line of best fit was found to be;

y = 23.875x + 279.625

where y denotes the total sales and x the corresponding week. We are required to determine y when x is 20;

Y = 23.875(20) + 279.625

y = 757.125

Therefore, the restaurant's sales for the Monday of the 20th week is expected to be $757.13