Question

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!

Answer 1

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.