Question

The data below shows the titles of ten movies from 2018, the production budget and domestic box office receipts (in millions). For example, Black Panther's budget was $200 million and the box office revenues in the US totaled $700 million.

Title	Production Budget	Domestic Box Office
Black Panther	200	700
Deadpool 2	110	325
A Star is Born	36	202
Vice	60	30
Crazy Rich Asians	30	175
Mary Poppins Returns	130	139
Creed II	50	114
Christopher Robin	75	99
Instant Family	48	66
Tag	21	60

The mean production budget is 76.00 and its standard deviation is 55.68.

The mean Domestic Box office revenue is 190.94 and its standard deviation is 198.10.

The correlation coefficient between the two variables is 0.81

[Useful formulas: slope=rSy/Sx and intercept = mean of Y – (slope * mean of X)]

I believe that movies that spend more in production end up receiving more in box office revenues.

You run a regression of BUDGET on DOMESTIC BOX OFFICE.

According to the regression, for each additional million dollars spent on the budget, do box office receipts increase or decrease?  

by how much? (only use one decimal place in your answer)

Answer 1

Let, Production Budget=X

Domestic Box Office=Y

According to the question,

=76 [Where, =Mean of Production Budget]

s.d(x)=55.68 [Where, s.d=standard deviation of production budget]

and,

=190.94 [Where, =mean of domestic box office]

s.d(Y)=198.10 [Where, s.d(Y)= standard deviation of Domestic box office]

Correlation coefficient between two variables r_x,y=0.81 i.e, correlation coeficient between Production Budget and Domestic box office

Now, using above informations we will determine the slope of the regression line.

slope()=

=

=0.227

The regression line of Production Budget (x) on Domestic Box Office(Y):

.......(1)

Putting values of , and in equation (1) we get the equation of regression line,

x=76+0.227(Y-190.94)

x=76+0.227Y-43.34

x=32.65+0.227 [here, Intercept=32.65]

• Hence, from the above equation of regression line we get, for each additional millions dollar spent on nthe budget, box office receipt increases.
• Box office receipt 0.227 for each millon dollar spent on production budget.