Question

Find the regression equation (rounding values to 2 places), letting the first variable be the independent variable x. Use the regression equation values to find the best predicted gross amount for a movie with a budget of 58 million dollars. Hint: Use the exact regression values to find an accurate predicted value and then round your answer.

In the table below, all amounts are in millions of dollars.

Budget 62 195 86 74 74 80 80 65

Gross 56 600 60 50 61 61 49 48

=	+ x
58 =

Answer 1

	( Budget ) X	( Gross ) Y	X * Y	X2	Y2
	62	56	3472	3844	3136
	195	600	117000	38025	360000
	86	60	5160	7396	3600
	74	50	3700	5476	2500
	74	61	4514	5476	3721
	80	61	4880	6400	3721
	80	49	3920	6400	2401
	65	48	3120	4225	2304
Total	716	985	145766	77242	381383

Equation of regression line is Ŷ = a + bX


b = 4.38
a =( Σ Y - ( b * Σ X) ) / n
a =( 985 - ( 4.3775 * 716 ) ) / 8
a = -268.67
Equation of regression line becomes Ŷ = -268.67 + 4.38 X

When X = 58
Ŷ = -268.665 + 4.378 X
Ŷ = -268.665 + ( 4.378 * 58 )
Ŷ = -14.74