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Mark​ Gershon, owner of a musical instrument​ distributorship, thinks that demand for guitars may be related...

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....

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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
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