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 |
a)
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.
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