Regression Analysis of Online Browsing Time and Age of Respondents

This assignment involves a statistical analysis of online browsing behavior. The student was tasked with analyzing data on the age of respondents, their sleep time, and the time they spend browsing online retailers per week. The analysis includes constructing a scatter diagram to visualize the relationship between age and browsing time, calculating and interpreting the correlation coefficient and the coefficient of determination. A simple regression equation was developed to predict browsing time based on age, and a regression line was plotted. The slope of the regression line was interpreted to understand the impact of age on browsing time. The model was then expanded to include sleep time as a second independent variable, and a comparison was made between the simple and multiple regression models to determine which provided a better fit for the data. The solution includes Excel outputs and interpretations of the statistical results.

Assignment 3

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a. Scatter diagram for the age of respondents as independent variable and browsing time (min/week) as
dependent variable.
Figure 1: Relation between age of respondents and browsing time (min/week) in a scatter diagram
Figure 1 represents a strong negative relation between age of respondents and browsing time
(min/week). With increase in age people are noted to surf internet for less time in a week. The relation
seems linear and the trend of linearity seems to be decreasing.
b. The correlation coefficient has been evaluated as R=-0 .963 , which indicates a strong and negative
association between age of respondents and weekly internet browsing time. The correlation is almost
perfectly negative (R = -1 is a perfect negative correlation), which indicates that internet browsing
time per week decreases in almost same proportion with increase in age (Mukaka, 2012, pp.69-71).
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c. The coefficient of determination R2=0 . 9275 indicates that age of respondents was able to explain
92.75% variation of weekly internet browsing time. It also indicated that the predicted values of
weekly browsing time are very close to the actual internet browsing time (Quinino, Reis, and
Bessegato, 2013, pp.84-88).
d. The simple regression equation has been provided in Table 1 and the regression line is plotted in
Figure 2.
Table 1: Excel Regression Output for estimating internet browsing time (min/week) by age of respondents
The regression line is evaluated as,
Browsing time (min/week) = -9.975*Age of respondents + 675.185.
The slope of regression line β=−9 . 975 indicates that for increase in age of respondents by one year
decreases the internet browsing time by approximately 9.98 minutes per week.
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Figure 2: Regression line for estimating internet browsing time (min/week) by age of respondents
e. The regression line is,
Browsing time (min/week) = -9.975*Age of respondents + 675.185.
Now Age of respondent = 57 years.
Hence, Browsing time (min/week) = -9.975*57 + 675.185 = 106.61 min/week.
Therefore, a 57 year person will most likely browse internet for approximately 107 minutes in week.
f. Sleep time (min/night) is added as a second independent variable in the previous simple regression
model. The new model has been represented in Table 2.
The coefficient of determination R2=0 . 93 indicates that age of respondents was able to explain 93.0%
variation of weekly internet browsing time. Hence, predictors in the new model are able to predict
almost 0.25% more variations in weekly internet browsing time.
The second model (multiple regression model) is preferable over the initial one (simple regression), as
it is able to explain more variations in internet browsing time.
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Table 2: Excel Regression Output for estimating internet browsing time (min/week) by age of respondents and sleep time (min/night)
References
Mukaka, M.M., 2012. A guide to appropriate use of correlation coefficient in medical research.
Malawi Medical Journal, 24(3), pp.69-71.
Quinino, R.C., Reis, E.A. and Bessegato, L.F., 2013. Using the Coefficient of Determination.
Teaching Statistics: An International Journal for Teachers, 35(2), pp.84-88.
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