Tran, owner of Flowers 4 You, operates a local chain of floral shops. Each shop

Question

Tran, owner of Flowers 4 You, operates a local chain of floral shops. Each shop has its own delivery van. Instead of charging a flat delivery fee,

Tran wants to set the delivery fee based on the distance driven to deliver the flowers.

Tran wants to separate the fixed and variable portions of her van operating costs so that she has a better idea how delivery distance affects these costs.

Flowers 4 You does a regression analysis on the next year's data using Excel. The output generated by Excel is as follows

SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations ANOVA 0.86 0.75 0.70 174.75 df MS 448,647.94 30,538.98 Significance F 14.69 Regression Residual Total 448,647.94 152,694.92 601,342.86 0.0122 Standard Lower Upper Coefficients 1028.28 0.26 Error t Stat P-value 95% 95% Intercept 1,131.33 0.91 0.41 -1,879.903,936.46 X Variable 1 0.07 3.83 0.01 0.09 0.43

Explanation / Answer

Tran, owner of Flowers 4 You, operates a local chain of floral shops. Each shop has its own delivery van. Instead of charging a flat delivery fee,

Tran wants to set the delivery fee based on the distance driven to deliver the flowers.

Tran wants to separate the fixed and variable portions of her van operating costs so that she has a better idea how delivery distance affects these costs.

Flowers 4 You does a regression analysis on the next year's data using Excel.

Here we have given regression output.

From the given output we can interpret the data as follows :

Regression equation :

y = 1028.28+ 0.26*X

where y is dependent variable and

x is independent variable.

Intercept = 1028.28

Slope = 0.26

Interpretation of slope : One unit change in x will be 0.26 unit increase in y.

Interpretation of intercept : If we take x is 0 then y will be 1028.28

Now we can test two significances :

i) Individual significance :

Now we can test the hypothesis that,

H0 : B = 0 Vs H1 : B not= 0

where B is population slope for x.

Assume alpha = level of significance = 0.05

The test statistic follows t-distribution.

t = 3.83

P-value = 0.01

P-value < alpha

Reject H0 at 5% level of significance.

Conclusion : The population slope for x is differ than 0.

We get significant result about t test.

ii) Overall significance :

Now we can test the hypothesis that,

H0 : Bj = 0 Vs H1 : Bj not= 0

where Bj is population slope for jth independent variable.

Assume alpha = level of significance = 0.05

The test statistic follows F-distribution.

F = 14.69

P-value = 0.0122

P-value < alpha

Reject H0 at 5% level of significance.

Conclusion : The population slope for jth independent variable is differ than 0.

We get significant result about F test.

R-sq = 0.75

It expresses the proporiton of variation in y which is explained by variation in x.

Multiple R = 0.86

It indicates that there is positive relationship between x and y.

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