Question

Movie companies need to predict the gross receipts of an individual movie once the movie has debuted. The data in the accompanying table are the first weekend​ gross, the regional​ gross, and the worldwide gross​ (in $millions) of six movies. Complete parts​ (a) and​ (b).

Title   First_Weekend   Regional_Gross   Worldwide_Gross
1 89.662 319.493 990.146
2 87.276 257.265 870.691
3 93.339 244.795 787.937
4 100.547 287.843 894.053
5 77.121 292.802 952.992
6 76.634 304.855 925.924

a. Compute the coefficient of correlation between first weekend gross and the regional​ gross, first weekend gross and the worldwide​ gross, and the regional gross and worldwide gross.

The coefficient of correlation between first weekend gross and the regional gross is

​(Round to four decimal places as​ needed.)

The coefficient of correlation between first weekend gross and the worldwide gross is

​(Round to four decimal places as​ needed.)

The coefficient of correlation between the regional gross and worldwide gross is

​(Round to four decimal places as​ needed.)

Identify the critical​ value(s)

Compute the test statistic for the linear relationship between first weekend gross and the regional gross.

tstat=

Compute the test statistic for the linear relationship between first weekend gross and the worldwide gross.

tstat=

Compute the test statistic for the linear relationship between the regional gross and worldwide gross.

tstat=

Answer 1

Using Minitab:

Correlation: First_Weekend, Regional_Gross, Worldwide_Gross First Weekend Regional_Gross Regional_Gross Worldwide_Gross -0.312 -0.413 0.931

The coefficient of correlation between first weekend gross and national gross.

r = -0.312

The coefficient of correlation between first weekend gross and worldwide gross.

r = -0.413

The coefficient of correlation between national gross and worldwide gross.

r = 0.931

test statistic for the linear relationship between first weekend gross and the regional gross.

t_stat $=r_{1}\sqrt{n-2}/\sqrt{1-r^{2}}$

$=-0.312\sqrt{6-2}/\sqrt{1-(-0.312)^{2}}$

  $=-0.691$

test statistic for the linear relationship between first weekend gross and the worldwide gross.

t_stat$=r_{1}\sqrt{n-2}/\sqrt{1-r^{2}}$

$=-0.413\sqrt{6-2}/\sqrt{1-(-0.413)^{2}}$

  $=-0.915$

test statistic for the linear relationship between the regional gross and worldwide gross.

tstat=

t_stat$=r_{1}\sqrt{n-2}/\sqrt{1-r^{2}}$

$=0.931\sqrt{6-2}/\sqrt{1-(0.931)^{2}}$

  $=2.063$

Hope this will be helpful. Thanks and God Bless You:)