The managers of a brokerage firm are interested in finding out if the number of new clients a broker brings into the firm affects the sales generated by the broker. They are presented in the table that follows. 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. These data are presented in the table that follows. 

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

a. Setup a scatter plot with the dependent variable on the vertical axis and independent variable on the horizontal axis. 

b. What is the lease squares estimate of the slope from the regression? 

c. Is the estimate of the slope significant at the 95% confidence level? Explain 

d. What does the slope estimate mean in relation to the problem facing the brokerage firm? 

e. What is the regression estimate on the Y-intercept? 

f. Is the estimate of the slope for the Y-intercept significant at the 95% confidence level? Explain 

g. What does the estimate of the Y-intercept mean in relation to the problem facing the brokerage firm?

h. How much in sales (in $1,000s) does the regression predict for a broker who brings 25 new clients into the firm? 

i. What percentage of the total variation in sales generated can be explained by the number of new clients brought in? 

j. What does the model predict for the case where the broker brings in 35 new clients?