Question

Arnold Tofu owns and operates a chain of vegetable protein "hamburger" restaurants in northern Louisiana. Sales figures and profits for the stores are in the table below.

Store Profits Sales

1    14      6

2    11     3

3    15      5

4     16     5

5     24    15

6     28    18

Calculate a regression line for the data and determine the forecast of profit for a store with sales of $24.

Answer 1

Answer:

Given data,

Store	Sales(X)	Profits(Y)	XY	X2	Y2
1	6	14	84	36	196
2	3	11	33	9	121
3	5	15	75	25	225
4	5	16	80	25	256
5	15	24	360	225	576
6	18	28	504	324	784

Equation of least square regression line is: Y = a + b X

Now, Slope (b) = (NΣXY - (ΣX)(ΣY)) / (NΣX² - (ΣX)²)

= (6 x 1136 - 52 x 108) / (6 x 644 - 52²) = 1.034

So, b = 1.034

Now, Intercept(a) = (ΣY - b(ΣX)) / N

= (108-1.034x52) / 6 = 9.038

So, the regression line is F_t = 9.038 + 1.034 X

So, Sales is $24 million, profit = 9.038 + 1.034 X 24 = $ 33.85