Stat 160 Postquiz 2, over Sections 1.8-1.10



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1. The following scatter diagram describes the relationship between number of new clients and sales amount of 10 brokers.
          -                                                       *
          -
        60+                                             *
          -                           *
  Sales   -                                        *
          -                              *
          -
        48+                                   *
          -
          -                                *
          -
          -                      *
        36+   *
          -          *
          -             *
          -          *
          -
            ----+---------+---------+---------+---------+---------+--Clients 
             12.0      18.0      24.0      30.0      36.0      42.0
Guess the correlation between number of clients and sales?
0.05
-0.32
0.74
4.25
2. The managers of a brokerage firm are interested in finding out if the number of new clients a broker brings into the firm is related to the sales generated by the broker. They sample 12 brokers and determine the number of new clients they have enrolled in the last year and their sales amounts in thousands of dollars. The data is given below
Broker  Clients  Sales
 
    1       27     52
    2       11     37
    3       42     64
    4       33     55
    5       15     29
    6       15     34
    7       25     58
    8       36     59
    9       28     44
   10       30     48
   11       17     31
   12       22     38

The following scatter diagram describes the relationship between number of clients and sales.

          -                                                       *
          -
        60+                                             *
          -                           *
  Sales   -                                        *
          -                              *
          -
        48+                                   *
          -
          -                                *
          -
          -                      *
        36+   *
          -          *
          -             *
          -          *
          -
            ----+---------+---------+---------+---------+---------+--Clients 
             12.0      18.0      24.0      30.0      36.0      42.0
What is the nature of the relationship between number of clients and sales?


As number of clients increases, the sales amount also increases.
As number of clients increases, the sales amount decreases.
As number of clients increases, the sales amount stays the same.
Impossible to determine.
3. Consider the situation in the previous problem. The following is the least squares regression line for the above sample:
	Sales = 17.7 + 1.12 Clients
What is the meaning of the slope estimate?


When the number of clients increases by 1, sales amount decreases by 17.7.
When the number of clients increases by 1.12, sales amount increases by 17.7.
When the number of clients increases by 1.12, sales amount increases by 1.
When the number of clients increases by 1, sales amount increases by 1.12.
4. Consider the situation in the previous problem. What is the practical meaning of the intercept estimate of 17.7?


It has no practical meaning because we have no data around zero clients.
We estimate 17.7 sales for a broker who has no clients.
When the number of clients increases by 17.7, sales amount increases by 1.
When the number of clients increases by 1, sales amount increases by 17.7
5. Consider again the situation in #3. Suppose we are also interested in the Wilcoxon fit. Which regression estimate (LS or Wilcoxon) will dramatically change if the last sales amount is changed from 38 to 380?


Both
Wilcoxon
Least squares
We cannot say