Question

Imagine you are a researcher for the Turonis Pizza Company interested in learning the effects of student population on quarterly sales. You collect sales data from a sample of 10 Turonis Pizza Parlor restaurants located near college campuses with known student populations. For the ith observation or restaurant in the sample, x is the size of the student population (in thousands) and y is the quarterly sales (in thousands of dollars). The values for x and y for the ten restaurants in the sample are summarized in the table located below:

Table: Student Population and Quarterly Sales Data for 10 Turonis Pizza Parlors

Restaurant i	Student Population (1000s) x	Quarterly Sales ($1000s) y
1	2	58
2	6	105
3	8	88
4	8	118
5	12	117
6	16	137
7	20	157
8	20	169
9	22	149
10	26	202

1. Create a scatter diagram of the data in the table above. Place student population on the horizontal axis and quarterly sales data on the vertical axis. What preliminary conclusions can be drawn from this scatter diagram?

2. BY HAND, calculate the simple regression equation that represents the relationship between quarterly sales and the student population. Then, predict the quarterly sales of a restaurant with a student population of 16,000.

Quarterly Sales (y) = b0 ± b1x (Student Population)

Answer 1

Create a scatter diagram of the data in the table above. Place student population on the horizontal axis and quarterly sales data on the vertical axis. What preliminary conclusions can be drawn from this scatter diagram?

From above scatterplot, we get to know there is a positive relationship exists between the student population and quarterly sales. If student population increases then the quarterly sales also increase and vice versa.

1. BY HAND, calculate the simple regression equation that represents the relationship between quarterly sales and the student population. Then, predict the quarterly sales of a restaurant with a student population of 16,000.

Quarterly Sales (y) = b0 ± b1x (Student Population)

	X	Y	XY	XX
	2	58	116	4
	6	105	630	36
	8	88	704	64
	8	118	944	64
	12	117	1404	144
	16	137	2192	256
	20	157	3140	400
	20	169	3380	400
	22	149	3278	484
	26	202	5252	676
Total	140	1300	21040	2528

The regression equation is:

Quarterly Sales (y) = b0 +b1x (Student Population)

Quarterly Sales (y) = 60 +5x (Student Population)

predict the quarterly sales of a restaurant with a student population of 16,000.

Answer: Put Student population =16

Quarterly Sales (y) = 60+ 5x (Student Population)

Quarterly Sales (y) = 60+ 5x 16

=60+80=140 or 140000