Question

For the following set of data, perform a regression analysis and answer the question. a) construct a scatter diagram b) determine the linear regression equation see what is a coefficient of correlation and what does it mean for this set of data? c)What is the coefficient of determination and what does it mean for this set of data? d)What is the standard error of the estimate and what does it mean? e)Estimate the revenue for the opening weekend for a movie if there are 3.5 million views of its trailer on YouTube?

Movie	Opening Weekend REvenue ($ Mill.)	Youtube Trailer Views (Mill.)
It comes at night	6.001	10.785
Pirates of the Caribbean: Dead Men tell no Tales	62.983	34.990
Baywatch	18.504	21.764
The circle	9.034	11.145
The Boss baby	50.199	52.292
The Belko Experiment	4.137	5.546
Collide	1.513	2.258
The founder	3.404	7.273

Answer 1

a)

Scatterplot - 10 20 30 40 50 60

b)

x	y	(x-x̅)²	(y-ȳ)²	(x-x̅)(y-ȳ)
10.785	6.001	55.83	181.46	100.65
34.99	62.983	280.01	1893.22	728.09
21.764	18.504	12.30	0.94	-3.39
11.145	9.034	50.58	108.95	74.23
52.292	50.199	1158.41	944.16	1045.81
5.546	4.137	161.56	235.16	194.92
2.258	1.513	255.96	322.52	287.32
7.273	3.404	120.64	258.18	176.48

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	146.053	155.775	2095.270668	3944.6	2604.10
mean	18.26	19.47	SSxx	SSyy	SSxy

sample size ,   n =   8          
here, x̅ = Σx / n=   18.26   ,     ȳ = Σy/n =   19.47  
                  
SSxx =    Σ(x-x̅)² =    2095.2707          
SSxy=   Σ(x-x̅)(y-ȳ) =   2604.1          
                  
estimated slope , ß1 = SSxy/SSxx =   2604.1   /   2095.271   =   1.2428
                  
intercept,   ß0 = y̅-ß1* x̄ =   -3.2183          
                  
so, regression line is   Ŷ =   -3.2183   +   1.2428   *x
                  
SSE=   (SSxx * SSyy - SS²xy)/SSxx =    708.087          
                  
std error ,Se =    √(SSE/(n-2)) =    10.863          
                  
correlation coefficient ,    r = Sxy/√(Sx.Sy) =   0.9058          

c)

Coefficint of determination= R² =    (Sxy)²/(Sx.Sy) =    0.8205

It means 82 % variance in revenue can be explained by youtube views.

d)

std error ,Se =    √(SSE/(n-2)) =    10.863

e)

Predicted Y at X=   3.5   is                  
Ŷ =   -3.21830   +   1.242846   *   3.5 =   1.132

Please revert back in case of any doubt.

Please upvote. Thanks in advance.