Regression Analysis
Introduction
This presentation on Regression Analysis will relate to a simple regression model. Initially, the regression model and the regression equation will be explored. As well, there will be a brief look into estimated regression equation. This case study that will be used involves a large Chinese Food restaurant chain.
Business Case
In this instance, the restaurant chain 's management wants to determine the best locations in which to expand their restaurant business. So far the most successful locations have been near college campuses. This opinion is based on the positive numbers that quarterly sales (y) reflect and the size of the student population (x). Management 's mindset is that over all, the restaurants that are within close proximity to college campuses with large student bodies generate more sales than restaurants located near campuses with small student bodies.
In the sample box below, xi is the size of the student population (in thousands) and yi is the quarterly sale (in thousands of dollars). The value for xi and yi for all of the 10 Chinese Food restaurants given in the sample are reflected as follows: Sample Data:
(measured in 1,000s) (measured in $1,000s)
Restaurant Student Population Quarterly Sales
(i) (xi) (yi)
1 2 58
2 6 105
3 8 88
4 8 118
5 12 117
6 16 137
7 20 157
8 20 169
9 22 149
10 26 202
Methodology
Given the circumstances, "in the simple linear regression model, y is a linear function of x (the β0 + β1 Xi part) plus єi. β0 and β1 are referred to as the parameters of the model, and є (the Greek letter epsilon) is a random variable referred to as the error term"
(Anderson, Sweeney & Williams, 2000, pg. 450). To state the simple linear equation succinctly; yi = β0 + β1x + єi. The yi equals the predicted value of Y for observation. Generally, the values for the parameters are unknown and therefore will require us to estimate them with
This presentation on Regression Analysis will relate to a simple regression model. Initially, the regression model and the regression equation will be explored. As well, there will be a brief look into estimated regression equation. This case study that will be used involves a large Chinese Food restaurant chain.
Business Case
In this instance, the restaurant chain 's management wants to determine the best locations in which to expand their restaurant business. So far the most successful locations have been near college campuses. This opinion is based on the positive numbers that quarterly sales (y) reflect and the size of the student population (x). Management 's mindset is that over all, the restaurants that are within close proximity to college campuses with large student bodies generate more sales than restaurants located near campuses with small student bodies.
In the sample box below, xi is the size of the student population (in thousands) and yi is the quarterly sale (in thousands of dollars). The value for xi and yi for all of the 10 Chinese Food restaurants given in the sample are reflected as follows: Sample Data:
(measured in 1,000s) (measured in $1,000s)
Restaurant Student Population Quarterly Sales
(i) (xi) (yi)
1 2 58
2 6 105
3 8 88
4 8 118
5 12 117
6 16 137
7 20 157
8 20 169
9 22 149
10 26 202
Methodology
Given the circumstances, "in the simple linear regression model, y is a linear function of x (the β0 + β1 Xi part) plus єi. β0 and β1 are referred to as the parameters of the model, and є (the Greek letter epsilon) is a random variable referred to as the error term"
(Anderson, Sweeney & Williams, 2000, pg. 450). To state the simple linear equation succinctly; yi = β0 + β1x + єi. The yi equals the predicted value of Y for observation. Generally, the values for the parameters are unknown and therefore will require us to estimate them with
References: Lind, D., Marchal, W. G., & Wathen, S.A. (2004). Statistical Techniques in Business and Economics (12e) McGraw Hill. Anderson, David R., Sweeney, Dennis J., Williams, Thomas A. Essentials of Statistics For Business And Economics (2nd edition) Southwestern College Publishing, 2000.