Yummy Lunch Restaurantneeds to decide the most profitable location for their business expansion. Marketing manager plans to use a multiple regression model to achieve their target. His model considers yearly revenue as the dependent variable. He found that number of people within 2KM (People), Mean household income(income), no of competitors and price as explanatory variables of company yearly revenue. The following is the descriptive statistics and regression output from Excel. Revenue People Income Competitors Price
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
Yummy Lunch Restaurantneeds to decide the most profitable location for their business expansion. Marketing manager plans to use a multiple regression model to achieve their target. His model considers yearly revenue as the dependent variable. He found that number of people within 2KM (People), Mean household income(income), no of competitors and price as explanatory variables of company yearly revenue.
The following is the
|
Revenue |
People |
Income |
Competitors |
Price |
|
|
Mean |
343965.68 |
5970.26 |
41522.96 |
2.8 |
5.68 |
|
Standard Error |
5307.89863 |
139.0845281 |
582.1376385 |
0.142857 |
0.051030203 |
|
Median |
345166.5 |
6032 |
41339.5 |
3 |
5.75 |
|
|
#N/A |
5917 |
#N/A |
3 |
6 |
|
Standard Deviation |
37532.51115 |
983.47613 |
4116.334718 |
1.010153 |
0.360838027 |
|
Sample Variance |
1408689393 |
967225.2984 |
16944211.51 |
1.020408 |
0.130204082 |
|
Sum |
17198284 |
298513 |
2076148 |
140 |
284 |
|
Count |
50 |
50 |
50 |
50 |
50 |
|
SUMMARY OUTPUT |
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|
Regression Statistics |
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|
Multiple R |
0.77 |
|||||||
|
R Square |
A |
|||||||
|
Adjusted R Square |
B |
|||||||
|
Standard Error |
25139.79 |
|||||||
|
Observations |
50.00 |
|||||||
|
ANOVA |
||||||||
|
|
df |
SS |
MS |
F |
Significance F |
|||
|
Regression |
C |
40585376295 |
F |
H |
3.0831E-08 |
|||
|
Residual |
D |
28440403984 |
G |
|||||
|
Total |
E |
69025780279 |
|
|
|
|||
|
|
Coefficients |
Standard Error |
t Stat |
P-value |
|
|||
|
Intercept |
-68363.1524 |
78524.7251 |
-0.8706 |
0.3886 |
|
|||
|
People |
6.4394 |
3.7051 |
I |
0.0891 |
|
|||
|
Income |
7.2723 |
0.9358 |
J |
0.0000 |
|
|||
|
Competitors |
-6709.4320 |
3818.5426 |
K |
0.0857 |
|
|||
|
Price |
15968.7648 |
10219.0263 |
L |
0.1251 |
|
You are required to;
c) What does the standard error of estimate tell you about the model?
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