# Regression Analysis

1301 Words Feb 16th, 2007 6 Pages
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.
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
Regression Analysis r² 0.903 n 10 r 0.950 k 1 Std. Error 13.829 Dep. Var. (yi) ANOVA table
Source SS df MS F p-value
Regression 14,200.0000 1 14,200.0000 74.25 2.55E-05
Residual 1,530.0000 8 191.2500
Total 15,730.0000 9

Regression output confidence interval variables coefficients std. error t (df=8) p-value 95% lower 95% upper
Intercept 60.0000 9.2260 6.503 .0002 38.7247 81.2753 (xi) 5.0000 0.5803 8.617 2.55E-05 3.6619 6.3381

The Regression Equation is Y = 60 + 5(X) for calculating what population results in what gross dollars in sales per restaurant. We will demonstrate the underlying math for this table in the following text with the sample data again broken down.
The coefficient of determination = .903 indicating a strong relationship between variables exists.

Sample data
(Table based on the least square criterion):

Restaurant (i) (xi) (yi) (xiyi) (xi2)
1 2 58 116 4
2 6 105 630 36
3 8 88 704 64
4 8 118 944 64
5 12 117 1,404 144
6 16 137 2,192 256
7 20 157 3,140 400
8 20 169 3,380 400
9 22 149 3,278 484
10 26 202 5,252 676 Totals 140 1,300 21,040 2,528 ∑xi ∑yi ∑xiyi ∑xi2

The following is the "least squares criterion" : min ∑( yi + ŷi)2 . As a result, the slope and y intercept for the estimated regression equation will