Question

7. Suppose GNC, a vitamin and supplement supplier, would like to investigate the relationship between the size of an order and the age of the consumer who ordered it. This information could allow GNC to target its promotions to specific age groups. The following table shows the ages for seven randomly selected customers along with the most recent order sizes in dollars (Assume that "Age" is the independent variable and "Order size" is the dependent variable) SHOW YOUR WORK Age Order Size (S) You can use the table below to help you with your calculations 22 yxyxy 2214 1681 2916 780 676 900 748 1156 484 63 34022916 3969 15 435841225 12252401 85 323014447225 25 625 38 a. Calculate the slope and y-intercept for the linear regression equation for the data above. (Please use formulas 14.7 and 14.8). b. Write the regression equation. c. In terms of "Age" and "Order Size" explain the slope you found in (a)

Please show formulas you use, it isn't multiple questions only 1. Teacher likes to break the question into multiple parts to help students with the steps. Thank you :)!

Answer 1

Computational Table:

	X	Y	X2	Y2	XY
	41	54	1681	2916	2214
	26	30	676	900	780
	34	22	1156	484	748
	54	63	2916	3969	3402
	29	15	841	225	435
	49	25	2401	625	1225
	38	85	1444	7225	3230
Total	271	294	11115	16344	12034

a)

x Σχι 271 - 38.71

☺ - Dvi _294 – 42 n

For Slope:

και ηΣΧΥ - (Σx)(ΣΥ) ηΣ Χ2 – (Σ Χ)2

b = 7*12034 - (271) (294) 7 * 11115 - (271)2

b = 1.05

Slope (b) = 1.05

For Intercept:

XI-X=

a = 42 - 1.05*38.71

a = 1.51

Intercept (a) = 1.51

b)

Therefore, the least square regression line would be,

* = a+b(X)

$\hat{Y}$ = 1.51 + 1.05(X)

C)

Interpret slope:

If the Age of the Customer is increased by 1 year then order size will increased by Approximately 1.05 dollars.

d) Predict size of order for a customer who is 40 years old.

We know that,

The least square regression line would be,

* = a+b(X)

$\hat{Y}$ = 1.51 + 1.05(X)

Plug X = 40 in above equation.

$\hat{Y}$ = 1.51 + 1.05*40

$\hat{Y}$= 43.34 $