Regression for Sale Unit of Men’s Wallet

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The relationships between “Customers” and “Comments”, “Comments” and “Collection Add” are very doubtful. So we need close observation during liner regression later.

Regression Analysis

1st Liner Regression

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As we all know, the P-value should be no more than 5%, so we removed “Operation Time” firstly which has the largest P-value.

2nd Liner Regression

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This time, we removed “Price”.

3rd Liner Regression

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Based on the same principle, we removed “Comments”.

4th Liner Regression

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From the result, we noticed that both “R Square” and “Adjusted R Square” are 66%, close to 1. And all the variables’ P-values are smaller than 5%. All meet the principles.

However, we remember the doubtful correlations among “Customers”, “Comments”, and “Collection Add”. So we calculated the correlation again.

Sales Volume (unit)

Region

Discount

Customers

Collection Add

Sales Volume (unit)

1

Region

0.113860313

1

Discount

-0.044780318

-0.040390387

1

Customers

0.810195757

0.091465071

-0.018051062

1

Collection Add

0.459024798

0.078729011

0.048421446

0.510088819

1

We noticed that the correlation between “Customers” and “Collection Add”. Although 51% is not more than 70% (meet the principle), it is also large improperly. So we removed “Collection Add” and ran the last liner regression.

5th Liner Regression

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Estimation and Check the model assumption

Regression statistics

R2 is 0.66, Adjusted R2 is 0.66. This regression statistics is not very high but enough, we could believe the regression model fit the data. The standard error, which is an estimation of standard deviation of the random noise, is 281.7.

Test significance for the regression model

First we set the null hypothesis and alternative hypothesis.

H0: β2=β4=β5=0; Ha: some of β≠0

The p-value is 1.06*10-250 at 0.05 significance level.

Test significance for p-value of variances

H0: β1=0; Ha: β1≠0, reject H0: β1=0 at 0.05 level.

Intercept:

T statistics of intercept = 3.08

P-value of intercept = 0.00209, which is less than 0.05 significance

Region:

T statistics of region = 2.81

P-value of region= 0.00507, which is less than 0.05 significance

Discount:

T statistics of discount = -2.07

P-value of discount = 0.03847, which is less than 0.05 significance

Customer:

T statistics of customer = 58.07

P-value of customer = 2.21*10-7, which is less than 0.05 significance

So all the coefficient of the variances are significant.

Check for regression assumption

- Multi-collinearity

Sales Volume (unit)

Region

Discount

Customers

Sales Volume (unit)

1

Region

0.113860313

1

Discount

-0.044780318

-0.040390387

1

Customers

0.810195757

0.091465071

-0.018051062

1

From the table above, we can see the correlations between variables are not very high, so there is no evidence for multi-collinearity.

- Heteroscedasticity

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From the residual plots above, we can see there is no evidence of heteroscedasticity.

- Normality

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We can