More Business Statisitics

More Business Statisitics

Module 2 – Chapter 6
#3. The human resources department at a large multinational corporation wants to be able to predict average salary for a given number of years experience. Data on salary (in$1000’s) and years of experience were collected for a sample of employees.
a) Which variable is the explanatory or predictor variable?
b) Which variable is the response variable?
c) Which variable would you plot on the y axis?

#8. A study finds that during blizzards, online sales are highly associated with the number of snow plows on the road; the more plows, the more online purchases. The director of an association of online merchants suggests the organization should encourage municipalities to send out more plows whenever it snows because, he says, that will increase business. Comment.

#11. For the bookstore sales data in Exercise 1, the correlation is 0.965
Exercise 1 data:
Number of sales people working Sales (in$1000)
2 10
3 11
7 13
9 14
10 18
10 20
12 20
15 22
16 22
20 26
x=10.4 y=17.6
SD(x)=5.64 SD(y)=5.34

a) If the number of people working is 2 standard deviations above the mean, how many standard deviations above or below the mean do you expect sales to be?
b) What value of sales does that correspond to?
c) If the number of people working is 1 standard deviation below the mean, how many standard deviations above or below the mean do you expect sales to be?
d) What value of sales does that correspond to?

#15. A CEO complains that the winners of his “rookie junior executive of the year” award often turn out to have less impressive performance the following year. He wonders whether the award actually encourages them to slack off.
a) Can you offer a better explanation?

#25. Scatterplots: Which of the scatterplots show:
a) Little or no association?
b) A negative association?
c) A linear association?
d) A moderately strong association?
e) A very strong association?
#26. Scatterplots, part 2: Which of the scatterplots show:
a) Little or no association?
b) A negative association?
c) A linier association?
d) A moderately strong association?
e) A very strong association?
#30. Matching, part 2: Here are several scatterplots. The calculated correlations are -0.977, -0.021, 0.736, and 0.951. Which is which?

#31. Pizza Sales and price: A linear model fit to predict weekly Sales of frozen pizza (in pounds) from the average Price ($/unit) charged by the sample of stores in the city of Dallas in 39 recent weeks is:
Sales = 141,865.53 – 24,369.49 Price.
a) What is the explanatory variable?
b) What is the response variable?
c) What does the slope mean in this context?
d) What does the y-intercept mean in this context? Is it meaningful?
e) What do you predict the sales to be if the average price charged was $3.50 for a pizza?
f) If the sales for a price of $3.50 turned out to be 60,000 pounds, what would the residual be?

#40. Salary by job type: At a small company, the head of human resources wants to examine salary to prepare annual reviews. He selects 28 employees at random with job types ranging from 01 = Stocking clerk to 99 = President. He plots Salary ($) against Job Type and finds a strong linear relationship with the correlation of 0.96%

The regression output gives:
Salary = 15827.9 + 1939.1 Job Type
a) Write a few sentences interpreting this model and describing what he can conclude from this analysis.
#54. Online clothing purchases: An online clothing retailer examined their transactional database to see if total yearly Purchases ($) were related to customers’ Incomes ($). (You may assume that the assumptions and conditions for regression are met.)
The least squares liner regression is:
Purchases = -3.16 + 0.012 Income
a) Interpret the intercept in the linear model.
b) Interpret the slope in the linear model.
c) If a customer has an Income of $20,000, what is his predicted total yearly Purchases?
d) This customer’s yearly Purchases were actually $100. What is the residual using this linear model? Did the model provide and underestimate or overestimate for the customer?