QUANT homework
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Exemplarreference.pdf
Exemplar: Homework 1 Quant 530 1
Homework 1 : Exemplar
1. Generate descriptive statistics tables for each variable. Discuss measures of
center, variability, skewness, kurtosis, and maximum and minimum values for
each variable individually (5pts). Discuss a comparison of the mean and
variability for both variables. (5 pts)
Table 1
Descriptive statistic tables
Approach 1 Approach 2
Mean 14.4 Mean 12.3
Standard Error 1.377259 Standard Error 1.452946
Median 14 Median 12
Mode 12 Mode 10 Standard Deviation 6.159289
Standard Deviation 6.497773
Sample Variance 37.93684 Sample Variance 42.22105
Kurtosis 0.110085 Kurtosis -0.74375
Skewness 0.337807 Skewness -0.08879
Range 24 Range 24
Minimum 4 Minimum 0
Maximum 28 Maximum 24
Sum 288 Sum 246
Count 20 Count 20
Measures of center Measures of the center provide an indication of what is likely the most typical number of
subscriptions sold when either sales approach is used. It can be seen from the Descriptive
Statistics tables that for both approach 1 and approach 2, the mean and median are close in
value. This suggests that the distribution of subscription sales under both approaches are near
bell in shape with most subscription sales remaining close to the typical value regardless of
approach used. Even so, the tables suggests that when approach 1 is applied, on average a
larger number of subscriptions will be sold than when approach 2 is applied.
Exemplar: Homework 1 Quant 530 2
Measures of variability
Given the near bell shape of both distributions, the Empirical Rule can be applied to provide a
range estimate for the percentage of subscriptions sold. That is for approach 1 and approach 2,
approximately 68% of the number of subscriptions sold are between (8.2, 20.6) and (5.8, 18.8)
respectively. Agents that are applying approach 1 are more likely and at a more consistent rate
sale a higher number of subscriptions that those who applied approach 2. Furthermore, it can
be seen from the Descriptive Statistics table that there have been agents who have not been
successful selling any subscriptions while applying approach 2. This has not occurred, as of yet,
when approach 1 has been applied. In fact, the highest selling agent applied approach 1 when
accomplishing this goal.
Kurtosis and Skewness
The reported skewness numbers indicate that distributions of subscription sales under both
approaches are fairly symmetric in shape suggesting a balance in the number of agents who sell
subscriptions over and below the expected number. In fact, the reported kurtosis values
suggest that it is not very likely that large percentages of agents will sell extremely poorly or
well, beyond what is considered typical, regardless of which approach is used.
2. Generate a histogram for each variable. Discuss the shape of the histogram.
(5pts)
Figure 1: Number of subscriptions sold using Approach 1
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Exemplar: Homework 1 Quant 530 3
Figure 2: Number of subscriptions sold using Approach 2
Shape of histograms
Although the reported mean and median numerical summaries suggested that both approaches
resulted in near bell shaped subscription sales distributions, closer to a bi-modal shaped
distribution can be seen in Figure 2 for subscriptions sold under the method of approach 2. This
suggests that the reported mean value of approximately 12 subscriptions sold for approach 2
may not be the best representation of the number of subscriptions that are likely to be sold by
agents using this approach. If fact, it might be worth examining under which conditions are
agents more likely to sell the high of 20 as opposed to the high of 10 subscriptions under this
method. If these conditions are easily replicated, then it is possible that approach 2 may be
considered as viable (or even more so) an approach to the sell of subscriptions as approach 1 is
suggested to be.
3. Calculate the correlation coefficient between the two variables. Interpret the
results (5 pts)
A correlation of approximately .7 suggest a moderately positive relation between the
subscription sales performance of an agent applying approach 2 and their performance when
applying approach 1. That is, in general we can expect that if an agent does well selling
subscriptions using approach 1, then there is a likely chance that they will also do well when
using approach 2. It’s possible that this may mean that it is not necessarily the talent of the
sales agent that is generating the sales differences observed but the actual use of the particular
approach. More investigation is needed.
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Exemplar: Homework 1 Quant 530 4
4. Select one of the variables to be explanatory and the other to be response.
Indicate your selection. Generate a scatter plot of the two variables. Interpret
the direction, form, and strength observed through examination of the data
pattern (5 pts)
Figure 3: Scatterplot of the relation between the number of subscriptions sold under approach 1 and approach 2
Figure 3 shows the dot pattern resulting when an agent’s sales performance using approach 1
(explanatory) is being evaluated for impact on their performance when using approach 2
(response). It appears from Figure 3 that a positive upward trending dot pattern is most
evident for low and high selling agents. That is, if agents sell subscriptions well or badly under
approach 1 they appear to be likely to also sell well or badly under approach 2. However that
same positive linear trend doesn’t appear to be as evident for those agents who tend to sell
near the mid-range of subscription levels around the reported mean value of 14.5 for approach
1. The dot pattern in that area appears more scattered and less systematically predictable.
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Exemplar: Homework 1 Quant 530 5
5. On the scatter plot in Excel, generate the regression line and the regression
equation. Re-Write the regression equation using the variable names. Write an
interpretation of the regression equation using the variable names and the
regression coefficient values. (5 pts)
Figure 4: Scatterplot of the relation between the number of subscriptions sold under approach 1 and approach 2 with regression equation included
The regression equation, (Approach 2 Sales) = .7(Approach 1 sales) + 2.3, suggests that for the typical
agent the change in the rate of a sales made under approach 1 is lower than under approach 2. In
other words, this suggests that more effort may be needed to generate a comparable number of
subscription sales using approach 1 than when using approach 2. Moreover, the equation suggests
that even the worst agent, that doesn’t successfully sale any subscriptions under approach 1 is likely on
average to sell approximately two subscriptions using approach 2.
y = 0.6959x + 2.2791
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