Question

The budget​ (in millions of​ dollars) and worldwide gross​ (in millions of​ dollars) for eight movies are shown below. Complete parts​ (a) through​ (c).

Budget, x Gross, y

206 253

205 302

200 423

199 688

182 688

175 1035

173 1878

168 1225

(a) Display the data in a scatter plot

​(b) Calculate the correlation coefficient r.

(c) Make a conclusion about the type of correlation.

Answer 1

(a) Display the data in a scatter plot

​(b) Calculate the correlation coefficient r.

x	y	xy	x^2	y^2
206	253	52,118	42,436	64,009
205	302	61,910	42,025	91,204
200	423	84,600	40,000	178,929
199	688	136,912	39,601	473,344
182	688	125,216	33,124	473,344
175	1035	181,125	30,625	1,071,225
173	1878	324,894	29,929	3,526,884
168	1225	205,800	28,224	1,500,625

correlation coefficient​ r = [n(xy) - xy] / [nx^2-(x)^2] [ny^2-(y)^2]

= [ 8*1172575 - 1508*6492] / [8*285964- 1508^2] * [8*7379564 - 6492^2]

= -409,336 / 13648*16890448

= -409,336 / 480125.85

= -0.8526

- .85

(c) Make a conclusion about the type of correlation.

If two variables are negatively correlated, then one variable increases as other will decreases. As we first plot scatter graph , it shows a downward trend, indicating negative correlation.