Question

1. 2.194 Comparing Global Internet Connections. In Exercise 2.120 we discuss a study in which the Nielsen Company measured connection speeds on home computers in nine different countries in order to determine whether connection speed affects the amount of time consumers spend online. Table 2.29 (by exercise 2.194 in the textbook) shows the percent of Internet users with a “fast” connection (defined as 2Mb or faster) and the average amount of time spent online, defined as total hours connected to the Web from a home computer during the month of February 2011. The data are also available in the dataset GlobalInternet. We are interested in looking at whether the percent of Internet users with a fast internet connection predicts the number of hours spent online.
   
   1. What is the explanatory variable? What is the response variable? Is each categorical or quantitative?
      
      
      
      
      
   2. What would a positive association mean between these two variables? Briefly explain why a positive relationship might make sense in this context.
      
      
      
      
      
      
      
      
      
   3. What would a negative association mean between these two variables? Briefly explain why a negative relationship might make sense in this context.
      
      
      
      
      
      
      
   4. Make a scatterplot with regression line, using connection speed as the explanatory variable and time online as the response variable. Include a screen shot of your Statkey output with your homework submission. What is the correlation?
      
      
   5. Are there any outliers? If so, indicate the country associated with each outlier and describe the characteristics that make it an outlier for the scatterplot.
      
   6. Eliminate the outliers you identified, and generate another scatterplot with regression line. Is the correlation strongly affected by the outliers?
      
      
      
      
   7. Find the regression equation for these variables with the outliers removed. Include a screen shot of your Statkey scatterplot with regression line with your homework submission, and write the regression equation here.
   8. Interpret the slope of the regression line in context. Remember that an interpretation must include a number and units, in a sentence that explains the meaning.
   9. Use the regression line to predict the number of hours spent online in Febrary 2011 in a country in which 65% of Internet users have a fast connection. Show your calculations.

Answer 1

a)

An explantory variable is type of independent variable

An response variable is type of dependent variable

Here response variable  variable is hours online and explantory variable is percent fast connection.

Categorical variables take category or label values and place an individual into one of several groups

quantitative variable can take on multiple numerical values.

Each variable is quantative variable

b)

Positive association means that

If one variable will increase other variable also will increase or as one variable will be decreased other variable also be decreased

c)

Negative  association means that

If one variable will increase other variable will decrease or as one variable will be decreased other variable will  be increased

d)

We will plot the scatter plot using the minitab with below mentioned steps

Enter data into minitab >Graph>Scatterplot>Simple>Ok>Y variable:time online>X variable:Connection speed>Ok

Scatter plot is shown below

From the above scatter plot we can observe that

There exists the positive relationship between the two variables

e)

There exists two outliers .Two extreme points of scatter plot graph are outliers

which are first and last country is an outlier

Because they are very distant from the other data points

So Switzerland and Brazil are Outliers

f)

If we will eliminate an outlier from the scatterplot

then there is positive relationship between these two variables.

We have to check whether correlation is affected by outliers

Let us find the correlation using  the MINITAB

ENTER data into MINITAB sheet > Stat > Basic Statistics > Correlation > Variables : select both the variables > do not click on display p-values > ok

Correlations: Percent Fast Connection, Hours Online

Correlation coefficient of Percent Fast Connection and Hours Online = -0.64

It is correlation with outlier.

Correlation without outlier = 0.95

There exists significant difference between correlation coeffcient

Yes correlation coefficient is strongly affected by outliers

Please post seperately for other parts