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 R-squared value and interpret it’s meaning?

0.97597921

2) What is the correlation coefficient and interpret it’s meaning?

0.9879166

3) 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):

Receipts = 7,310.82

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

5) Do you accept or reject the null hypothesis?

6) 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

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.987917
R Square	0.975979
Adjusted R Square	0.971175
Standard Error	1830.236
Observations	7
ANOVA
	df	SS	MS	F	Significance F
Regression	1	6.81E+08	6.81E+08	203.153	3.06E-05
Residual	5	16748821	3349764
Total	6	6.97E+08
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	6808.105	854.9682	7.962991	0.000504	4610.339	9005.87	4610.339	9005.87
x	0.050272	0.003527	14.25318	3.06E-05	0.041205	0.059338	0.041205	0.059338

so, regression line is   Ŷ =   6808.105 +   0.050272 *x

3)

Predicted Y at X=   100000   is                  
Ŷ =   6808.10470   +   0.050272   *   100000   =   11835.259

4)

Ho:   ß1=   0          
H1:   ß1╪   0          
n=   7              
alpha =   0.05              
estimated std error of slope =Se(ß1) = Se/√Sxx =    1830.236   /√   269273194950.00   =   0.0035
                  
t stat = estimated slope/std error =ß1 /Se(ß1) =    0.0503   /   0.0035   =   14.2532
                  
Degree of freedom ,df = n-2=   5              
p-value =    0.0000              
decison :    p-value<α , reject Ho  

SO there IS significant evidence of a relationship between Twitter activity and receipts

           
5)

WE will reject the null hypothesis concluding that there is linear relationship

6)

from above ,

we can say that for a movie, the twitter activity and receipts are linearly related. As the twitter activity increases the receipt will also increase and vice versa

the twitter activity explain the response of receipts.