Question

There is a lot of competition for companies that try to attract new users of social media today since advertising dollars are involved. Facebook is one of these companies and it is one of the largest social media companies in the world. It was recently announced that Facebook broke the 2 billion mark in monthly users worldwide.

Facebook: number of monthly active users world wide 2008-2017
Quarters	Number in millions
Q4 '08	100
Q1 '09	197
Q2 '09	242
Q3 '09	305
Q4 '09	360
Q1 '10	431
Q2 '10	482
Q3 '10	550
Q4 '10	608
Q1 '11	680
Q2 '11	739
Q3 '11	800
Q4 '11	845
Q1 '12	901
Q2 '12	955
Q3 '12	1,007
Q4 '12	1,056
Q1 '13	1,110
Q2 '13	1,155
Q3 '13	1,189
Q4 '13	1,228
Q1 '14	1,276
Q2 '14	1,317
Q3 '14	1,350
Q4 '14	1,393
Q1 '15	1,441
Q2 '15	1,490
Q3 '15	1,545
Q4 '15	1,591
Q1 '16	1,654
Q2 '16	1,712
Q3 '16	1,788
Q4 '16	1,860
Q1 '17	1,936

1. Which variable should be the dependent variable and which should be the independent variable? Why

2.Put the data into excel.

3. Does the line seem to fit the data? Why?

4. Calculate the following use excel trendline:

1. y-intercept to two decimal places a=
2. slope to 3 decimal places B=

5. correlation coefficient (to 4 decimal places) =
6. n =
7. correlation of determination (to 3 decimal places) =

3. line of best fit equation y =

8. What does the correlation imply about the relationship between the time and the number of users?
9. Is the correlation significant? Why or why not? (Answer in 1-2 complete sentences.) (Use the Pearson calculator).
10. Interpret the coefficient of determination in this real world context:
11. Can the regression line be used for prediction?

Answer 1

Year should be the dependent variable and number of users should be the independent variable. As the number of users are growing with time. Hence, the number of users dependent on years.

2. Put the data into the excel sheet:

The quarter Q4,08 is considered as 1st quarter and number goes further accordingly.

3. Scatter plot needs to created using excel

Step 1: Go to insert --> scatter plot --> select the data

Step 2: Go to plus option at the top right hand side and add the trend line

Yes, the line seems to fit the data as the data looks linear.

4. The regression equation needs to be created.

Step: Go to data --> data analysis --> regression

Step 2: Click regression --> select the data --> get the output

The standard regression is of the form:

y = a + bx

where,

a = intercept

b = slope

As per output, the equation will be:

y = 416.374 + 40.565x

Intercept (a) = 416.374

Slope = 40.565

Correlation coefficient(R value) = 0.63

n = 34

Coefficient of Determination (R square) = 0.396

line of best fit equation, y = 416.374 + 40.565x

The correlation coefficient indicates that there is highly positive relationship between time and number of users.

Yes, the correlation is significant because the p-value of intercept (0.02) is less the assumed level of significance (0.05)

The coefficient of determination (0.3969) indicates that 39.696 % of the variation in number of users is explained by the time.

By considering other practical factors, the regression equation can not be used for prediction because the number of users are dependent on other factors also along with time.