Assignment 2
Problem #1
Part A.
Complete the frequency distribution table, calculating the number of occurrences for each of the frequency intervals (bins) of the given three variables:
Part B.
We know that a value is not an outlier if it is between Q1 - 1.5IQR and Q3 + 1.5 IQR. Calculate Q1, Q3 and IQR:
The following values are not outliers:
Donating – from 0 to 74
Helping – from 14 to 83
Volunteering – from 0 to 53
Based on this, we can conclude that there are three outlier values in donating score: 91, 78 and 77. These are extremely high values.
Part C.
The distributions of Donating and Volunteering scores are skewed to the left. For skewed distribution, we use median and IQR as measures of central tendency and variability. The distribution of Helping Score is approximately symmetric. We use mean and standard deviation for non-skewed distribution.
Boxplots indicate the same values of outliers that we have determined in part B. They support our previous analysis.
Part D.
It seems that Helping activity appears more often than the other two types of giving activities among the 135 countries considered. According to the boxplots, on average, approximately 50% of people help a stranger. The mean percentages of the other two activities are approximately equal – around 20% for both Donating and Volunteering. However, Donating percentage is more dispersed than Volunteering. In Australia, 37% of respondents participated in Volunteering, 65% of respondents helped strangers and 66% of respondents donated. Australia indicators are significantly higher than the mean percentages level in the sample. Australians’ propensity to giving is above the average level. The level of donating and helping is high and approximately equal, the level of volunteering is lower but still higher than average.
Problem #2
Part A.
Stacked chart is presented in .xls file.
Part B.
This probability is the ratio between the number of all participants and the number of those who choose to participate in a fundraiser:
2761570=0.176
Part C.
These probabilities are given in the table below:
Part D.
The probability of choosing mobile way:
1441570=0.0917
These probabilities are given in the table below:
Part E.
The most usual ways of giving among generation Y are by mobile, social networks and fundraiser. They almost do not use mail for giving activities. People of generation X are most likely to give donation through the workplace. Mail is also almost not used by this generation group. However, mailing takes 1st place by popularity among Baby Boomers and Matures.
Problem #3
Part A.
The decision variables are the numbers of various types of ads using. Let the number of radio spots is r, the number of bundles of flyers is f and the number of newspapers is n.
The objective function is the number of people reached by ads. In other words, this function can be expressed as:
5000r+2400f+2800n
This is a maximization problem.
Constraints are the following.
Budgeting constraint:
800r+240f+320n≤8000
Radio spots number constraint:
r≤12
Flyers number constraint:
f≤25
Newspapers number constraint:
n≤20
Print-based ads number constraint:
f+n≥5
Expenditures on print advertising constraint:
240f+320n≤2400
Non-negativity constraint:
r,f,n≥0
Part B
Part C
Shadow prices indicate that each additional dollar in the budgeting constraint will result in additional 6.25 persons in reached audience. An additional dollar spent on print ads results in 3.75 additional persons in reached audience.
Part D
Yes, it will change. Shadow price allowable increase section helps me to answer this question.
Part E
Yes, the solution will be changed. Shadow Price and allowable increase help to answer this question. The new result is below:
Part F.
Under the initial conditions, we have to place 7 radio spots and 10 bundles of flyers. No newspaper ads needed. This will reach the audience of 59000 individuals. In order to increase the number of individuals reached by our ads, we may either increase the budget or increase spending on print advertising.
Problem #4
Part A
It seems that the points are located closely to a straight line. It should be appropriate to fit a regression line in this case.
Part B.
Without unique visits, the number of online orders is estimated at 79.5. An additional thousand of unique visits increase the number of online orders by 75.2 orders. Coefficient of determination shows the percent of variance of online orders variable, explained by unique visits variable. Approximately 84% of variance is explained by this model, 16% of variance left unexplained.
Part C
Predict the number of orders for 800000 unique visitors:
0.0752*80 + 0.795 = 6.811
The estimated number of orders is 681.1
Part D
There is a positive association between the variables. Additional unique visitors result in the increase of the number of online orders. The regression equation has been developed in order to describe the relationship mathematically.
