Question

To study how social media may influence the products consumers​ buy, researchers collected the opening weekend box office revenue​ (in millions of​dollars) for 23 recent movies and the social media message rate​ (average number of messages referring to the movie per​ hour). The data are available below. Conduct a complete simple linear regression analysis of the relationship between revenue​ (y) and message rate​ (x).

Message Rate Revenue​ ($millions)

1363.2 146

1219.2 79

681.2 67

583.6 37

454.7 35

413.9 34

306.2 21

289.8 18

245.1 18

163.9 17

148.9 16

147.4 15

147.3 15

123.6 14

118.1 13

108.9 13

100.1 12

90.3 11

89.1 6

70.1 6

56.2 5

41.6 3

8.4 1

The least squares regression equation is ModifyingAbove y with carety=________ +(_________) ​(Round to three decimal places as​ needed.)

Answer 1

I believe the sample is

Message Rate	Revenue
1363.2	146
1219.2	79
681.2	67
583.6	37
454.7	35
413.9	34
306.2	21
289.8	18
245.1	18
163.9	17
148.9	16
147.4	15
147.3	15
123.6	14
118.1	13
108.9	13
100.1	12
90.3	11
89.1	6
70.1	6
56.2	5
41.6	3
8.4	1

the regression equation for Y is calculated as

Regression Equation = ŷ = bX + a
where,

Sum of X = 6970.8
Sum of Y = 602
Mean X = 303.0783
Mean Y = 26.1739
Sum of squares (SS_X) = 2822097.8591
Sum of products (SP) = 244004.487

and

b = SP/SS_X = 244004.49/2822097.86 = 0.08646

a = M_Y - bM_X = 26.17 - (0.09*303.08) = -0.03087

hence

ŷ = 0.08646X - 0.03087

The least squares regression equation is ModifyingAbove y with carety=0.086*X+(-0.031)