Question

Listed below are the budgets​ (in millions of​ dollars) and the gross receipts​ (in millions of​ dollars) for randomly selected movies. Construct a​ scatterplot, find the value of the linear correlation coefficient​ r, and find the​ P-value using alphaαequals=0.05 Is there sufficient evidence to conclude that there is a linear correlation between budgets and gross​ receipts? Do the results change if the actual budgets listed are $​64,000, ​$85,000​ $47,000 and so​ on?

Budget​ (x)	64	85	47	36	194	100	87
Gross​ (y)	70	69	46	61	603	140	51

linear correlation coefficient r?

T stat?

P-value?

Because P-value is greater or lesser, it has enough or doesn't have enough evidence?

Do the results change from the budgets listed?

Answer 1

S.No	X	Y	(x-x̅)2	(y-y̅)2	(x-x̅)(y-y̅)
1	64	70	555.6122	6173.4694	1852.0408
2	85	69	6.6122	6331.6122	204.6122
3	47	46	1646.0408	10520.8980	4161.4694
4	36	61	2659.6122	7668.7551	4516.1837
5	194	603	11327.0408	206505.3265	48364.1837
6	100	140	154.4694	73.4694	-106.5306
7	87	51	0.3265	9520.1837	55.7551
Total	613	1040	16349.7143	246793.7143	59047.7143
Mean	87.571	148.571	SSX	SSY	SXY

correlation coefficient r=

Sxy/(√Sxx*Syy) =

0.930

test stat t=

r*(√(n-2)/(1-r2))=

5.638~ 5.64

P value    =

0.0012~ 0.001

Because P-value is  lesser, there is sufficient evidence,,,,,,,,,

No they will not change