Question

In: Statistics and Probability

Movie Twitter Activity Receipts The Devil Inside 219509 14763 The Dictator 6405 5796 Paranormal Activity 3...

Movie

Twitter Activity

Receipts

The Devil Inside

219509

14763

The Dictator

6405

5796

Paranormal Activity 3

165128

15829

The Hunger Games

579288

36871

Bridesmaids

6564

8995

Red Tails

11104

7477

Act of Valor

9152

8054

  1. What is the independent variable (X) and what is the dependent variable (y)

B. Write a null and alternative hypothesis statement

C. What is the R-squared value and interpret it’s meaning?

D. What is the correlation coefficient and interpret it’s meaning?

E. Predict the receipts for a movie that has a Twitter activity of 100,000 using the linear regression formula generated after you run the regression analysis in Excel (just like we did in the lecture notes)

F. At the 95% significance level, is there significant evidence of a relationship between Twitter activity and receipts?

G. Do you accept or reject the null hypothesis?

H. Based upon your answers above, provide us with a paragraph (3-4 sentence) conclusion that would be appropriate to explain the results to a senior executive that isn’t as familiar with statistics as you are!

Solutions

Expert Solution

Output using excel:

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.279643
R Square 0.0782
Adjusted R Square -0.10616
Standard Error 11337.88
Observations 7
ANOVA
df SS MS F Significance F
Regression 1 54526187.0403 54526187.0403 0.424172 0.543606
Residual 5 642737346.3883 128547469.2777
Total 6 697263533.4286
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 11648.22 5573.582 2.089898 0.090912 -2679.133 25975.57
X 0.034148 0.052432 0.651285 0.543606 -0.100633 0.16893

a) Independent variable (X) = Twitter Activity

Dependent variable (y) = Receipts

b) Null and alternative hypothesis:

Ho: ρ = 0

Ha: ρ ≠ 0

c) Coefficient of determination, r² = 0.0782

7.82% variation in y is explained by the least squares model.     

d) Correlation coefficient, r = 0.2796

It indicates there is a positive weak relationship between x and y.

e) Regression equation :   

ŷ = 11648.217 + (0.0341) x  

Predicted value of y at x =    100000

ŷ = 11648.217 + (0.0341) * 100000 = 15063.0599

f) Correlation, r = 0.2796

Test statistic :    

t = r*√(n-2)/√(1-r²) = 0.2796 *√(7 - 2)/√(1 - 0.2796²) =    0.6513

df = n-2 =    5

p-value = T.DIST.2T(ABS(0.6513), 5) = 0.5436

g) Conclusion:  

p-value > α , Fail to reject the null hypothesis.

h) We fail to reject the null hypothesis.so, we can say that there is no correlation between x and y.


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