Question

Mark​ Gershon, owner of a musical instrument​ distributorship, thinks that demand for guitars may be related to the number of television appearances by the popular group Maroon 5 during the previous month. Gershon has collected the data shown in the following​ table:

                                                                                                          

Maroon 5 TV Appearances	33	55	66	77	77	66
Demand for Guitars	33	55	88	44	1010	77

This exercise contains only parts​ b, c, and d.

​b) Using the​ least-squares regression​ method, the equation for forecasting is ​(round your responses to four decimal

​places)​:

Y​ =  .... ​+ .... x

- THIS QUESTION HAS EXTRA STEPS SO PLEASE BE PREPARED TO ANSWER THE OTHER PARTS AS WELL....

Answer 1

Use the least-squares regression method to derive a forecasting equation
Maroon 5 TV Appearances (x)	Demand for Guitars (y)	X^2	XY
33	33	1089	1089
55	55	3025	3025
66	88	4356	5808
77	44	5929	3388
77	1010	5929	77770
66	77	4356	5082
374	1307	24684	96162
Σx = 374	Σy = 1307	Σx^2 = 24684	Σxy = 96162
N (number of data values) = 6
y = b + mX
Let us find the best m (slope) and b (y-intercept) that suits that data
Slope m = N Σ(xy) − Σx Σy /N Σ(x^2) − (Σx)^2
Slope m = (6 x 96162) −374 x 1307 /6 x 2468 − (374)^2	10.7139
Intercept b
b = Σy − m Σx/N
b = (1307 − 10.71 x  374)/6	-450.0000
Y = -450 + 10.71 X