# Homework 3 (R language and statistical background needed)

Instruction:

For this assignment, we will be working on understanding the behaviors and characteristics of people who use a digital application related to health and wellness. A free version offers limited content, such as tracking your exercise. A paid subscription service offers personalized coaching from a certified exercise trainer.  The company generally values the utilization of the application.  The product managers want the users to sign in frequently.  Paid coaching is a source of revenue for the company.  The product managers are also interested in analyzing their data to better understand the patterns of user behaviors.  Your work on this assignment will support that effort.

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Data:

To begin to investigate these questions, the company has gathered some information(exercise_application_user_data.csv attached below) The data include a sample of new users of the application. Each user.s behavior was tracked for 90 days. For each user, basic demographic information (Age.Group and Country) was collected from the user’s profile. Then the following characteristics were measured:

Weekly.Exercise.Sessions: This records an individual user’s rate of weekly exercise sessions tracked in the application over the 90 day period.

Daily.Logins: This measures the user’s rate of logins per day over the 90 day period.

Paid.Coaching: This measure (TRUE/FALSE) indicates whether the user paid for any coaching service within 90 days.

Based on the information above and the data provided, please answer the following questions. For multiple choice questions, please select the best answer.  When numeric answers are requested, enter the value to at least 4 decimal places. For questions with a free response, please answer in approximately 2-4 sentences. Your answers should be directed to the product manager of the digital application.

So far, we’ve covered linear and logistic regression, so please do not go beyond these two areas. Please also provide R code and brief explanations with the answers, thank you.

Logistic Regression and Odds Ratio Example:
A survey was conducted among 600 teenagers to determine if college graduation is
related to the likelihood of wearing a seatbelt when in a motor vehicle (beltalways). The
primary outcome (dependent variable) was whether a seatbelt was always worn (coded
0 for no and 1 for yes). The main independent variable was college graduate (grad)
sex (sexm) (coded 0 for no and 1 for yes).
Because the variables are categorical (binary), we use multiple logistic regression
analysis using the “glm” function in R (general linear models). “glm” includes different
procedures so we need to add the code at the end “family=binomial (link=logit)” to
indicate logistic regression. We can conduct the logistic analysis using the code below:
>log.out summary(log.out)
The default output shows the regression slopes which can be used to judge the
direction of associations and their statistical significance. Note that grad has a positive
association with wearing seatbelts and sexm has a negative association with wearing
seatbelts.
Coefficients: Estimate Std. Error z value Pr(>|z|)
(Intercept). -1.31109 0.84639 -1.549 0.121376
sexm
– 0.15505 0.17060 -0.909 0.363414
0.17192 0.07599 2.262 0.023672 *
We need to exponentiate the coefficients in order to get the odds ratios. R can do this
with the following command:
> exp(log.out\$coeff)
(Intercept)
sexm
0.2695271 0.8563720 1.1875858
Interpreting this Odds Ratios
In this case, the outcome is wearing a seatbelt. Males were 14% less likely to wear a
seatbelt, but the difference was not statistically significant (p=0.36). College graduates
were 19% more likely to wear a seatbelt (p=0.024).
Remember: When variables show to have a negative association with the outcome
variable – when it is converted into an Odds Ratio it will be less than 1. (sexm). When
variables show to have a positive association with the outcome variable – when it is
converted into an Odds Ratio it will be greater than 1. (grad).

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