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# Regression, Test of Hypothesis, and Correlation

1) Car dealership chain owner wants to increase the car sales of his chain. He wants to determine which factors influence the sales performance. Owner thinks that the following factors have a significant impact on sales performance:

X1 = number of years of experience as a car sales person
X2 = age

Sales performance is measured as number of cars sold per year Y.
Owner selects twenty sales associates at random. Their past sales performance, number of years of experience, and age were retrieved from dealership records. Owner hires a statistician who enters the data into statistical software package and the following equation is obtained:

Y' = 9.606 + 1.998X1 + 0.222X2

A. How is this equation called?

B. How many independent variables are there in this equation? How many dependent variables?

C. What is the number 1.998 called?

D. As number of years of experience (X1) increases for one year, how much will estimated number of cars sold per year increase.

E. Michael Pendergrass applied for a sales associate position. He has been a car salesman for ten years and he is 37 years old. Estimate annual numbers of cars per year Michael would sell if he was hired.

2) Two Internet Service Providers companies in the Greensboro, NC area compete for customers. In order to select the better provider, we want to test whether there is a difference in the proportion of times a customer is able to access the Internet. We have attempted to connect to the server of the first provider 500 times, and were able to access the Internet on 455 occasions. Then we attempted to make a connection with the second provider, and were able to connect on 344 of 400 trials. At the 0.05 significance level, is there a difference in percentages of success between these two ISPs?

3) Recent medical research demonstrated there is a strong (r=.60) correlation between the excessive weight and incidences of breast cancer. How can we interpret this statement? Can we say that excessive weight is the leading cause of breast cancer? How confident can we be about the strength of the relation between these two variables? Can we conclude that the correlation observed on the sample is also the population correlation coefficient?
* Even though the correlation between obesity and breast cancer actually exists, r of 0.60 is a fictitious number.

#### Solution Preview

Car dealership chain owner wants to increase the car sales of his chain. He wants to determine which factors influence the sales performance. Owner thinks that the following factors have a significant impact on sales performance:
X1 = number of years of experience as a car sales person
X2 = age
Sales performance is measured as number of cars sold per year Y.
Owner selects twenty sales associates at random. Their past sales performance, number of years of experience, and age were retrieved from dealership records. Owner hires a statistician who enters the data into statistical software package and the following equation is obtained:
Y' = 9.606 + 1.998X1 + 0.222X2
A. How is this equation called?
B. How many independent variables are there in this equation? How many dependent variables?
C. What is the number 1.998 called?
D. As number of years of experience (X1) increases for one year, how much will estimated number of cars sold per year increase.
E. Michael Pendergrass applied for a sales associate position. He has been a car salesman for ten years and he is 37 years old. Estimate annual numbers of cars per year Michael would sell if he was hired.

A. How is this equation called?

This equation is called the REGRESSION EQUATION

B. How many independent variables are there in this equation? How many dependent variables?
There are two independent variables: X1 and X2
X1 = number of years of experience as a car sales person
X2 = age
There is one dependent variable Y (number of cars sold per year)

C. What is the number 1.998 called?

The number 1.998 is called the regression coefficient for X1

D. As number of years of experience (X1) increases for one year, how much will estimated number of cars sold per year increase.

Since
Y' = 9.606 + 1.998X1 + 0.222X2
A unit increase in X1 will increase the number of cars sold per year by 1.998

E. ...

#### Solution Summary

Answers questions on Regression, Test of hypothesis for difference in proportions, Correlation.

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