Yummy Lunch Restaurant needs 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 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 Mode #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 Regression Statistics 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 Please find: Complete the missing entries from A to L in this output Derive the regression model What does the standard error of estimate tell you about the model Assess the independent variables significance at 5% level (develop hypothesis if necessary in the analysis)?
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 Restaurant needs 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),
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 |
|
|
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 |
|
|
Regression Statistics |
|
|
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 |
Please find:
Complete the missing entries from A to L in this output
Derive the regression model
What does the standard error of estimate tell you about the model
Assess the independent variables significance at 5% level (develop hypothesis if necessary in the analysis)?
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