Question

1. Which variable should be the dependent variable and which should be the independent variable? Why?
2. Plot the points on the scatterplot graph. NOTE: In a scatterplot the x axis will always reflect 1, 2, 3… not the Quarters specifically.

Label both axes with words.

In order to analyze the data we will use the line of best fit.

1. Answer with 1-3 complete sentences. Does the line seem to fit the data? Why?

2. 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) =
8. line of best fit equation
9. What does the correlation imply about the relationship between the time and the number of users?

10. Is the correlation significant? Why or why not? (Answer in 1-2 complete sentences.) (Use the Pearson calculator).

11. Interpret the coefficient of determination in this real world context:

12) Can the regression line be used for prediction?

13. Predict the following:

1. For the First quarter of 2008, predict the total monthly users.
2. For the First quarter of 2020, predict the total monthly users.

Quarter	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

Answer 1

Answer:

Dependent variable: Number in millions

Independent variable: Period (Quarterly)

Explanation:

Since we want to predict the number of users (in million) based on the quarterly time, the number depends on the period. Hence the number of users is a dependent variable and the quarterly time is the independent variable.

Scatterplot

Answer:

Explanation:

The scatterplot is obtained in excel by following these steps,

Step 1: Write the data values in excel. The screenshot is shown below,

Step 2: Select the time and Number of users columns then go to the graph area then INSERT > Recommended Chart > XY Scatter > OK.

Line of best fit.

Answer:

From the scatterplot, we can observe that there is a positive linear trend between and the number of users and the quarterly time. There is a strong association between the two variables which means the data values are aligned in a straight line that is why the linear trendline fits the data values very well.

y-intercept, a= 127.604

Slope to 3 decimal places, b= 52.024

The correlation coefficient, r = 0.9976

n = 34

The correlation of determination, r^2 = 0.995

line of the best-fit equation

There is a very strong positive linear correlation between the time and the number of users.

The t-test from the parameter estimation table shows that the slope coefficient is statistically significant at a 5% significance level (i.e. p-value = 1.31E-18 < 0.05) which indicates that there is a significant positive association between the time and the number of users.

The coefficient of determination (R-square value) tells, how well the regression model fits the data values. The R-square value of the model is 0.9952 which means, the model explains approximately 99.52% of the variance of the data value. Based on this evidence we can conclude the model is a good fit.

Hence we can predict the number of users based on the time very accurately.

Explanation:

The best fit line and the regression analysis is done in excel by following these steps,

Step 1: Write the data values in excel. The screenshot is shown below,

Step 2: DATA > Data Analysis > Regression > OK. The screenshot is shown below,

Step 3: Select Input Y Range: 'Number of users' column, Input X Range: 'Time' column, and select the Line Fit Plots then OK. The screenshot is shown below,

The result is obtained. The screenshot is shown below,

Best-fit line

the regression equation is defined as,

where a = intercept and b = slope of the best-fit equation

From the regression output summary,

Correlation coefficient

From the regression output summary,

Multiple R

0.997573

Correlation of determination

From the regression output summary,

R Square

0.995151

Prediction

Answer:

For first-quarter of 2008 => total monthly users = 23.556 millions

For first-quarter of 2020 => total monthly users = 2520.722 millions

Explanation:

The regression equation is,

For first-quarter of 2008 => Time = -2

For first-quarter of 2020 => Time = 46