Business Case on Pronto Pizza

July 10, 2017 | Author: Muhammad Bilal | Category: Errors And Residuals, Statistical Theory, Statistical Inference, Statistics, Estimation Theory
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Business Case on Pronto Pizza Introduction: Pronto Pizza is a family owned pizza restaurant in Vinemont, a small town of 20,000 people in upstate New York. Antonio Scapelli started the business 30 years ago as Antonio’s Restaurant with a few thousand dollars. Antonio, his wife, and their children, most of who are now grown, operate the business. Many years ago Antonio’s son Tony Jr, graduated from NYU with an undergraduate degree in Business administration. This Pronto Pizza was one of earliest pizza restaurant which offered home delivery. Fortunately, Tony had the foresight of this business decision a few years ago. At the same time Tony changed the name of this business from Antonio’s to Pronto Pizza. Nearly 90% of the Pronto’s current business is derived from Pizza delivery service.

Analysis: Solution 1 Coefficient of co-relation ( r )

0.9359

The sign of coefficient of corelation (r) is positive. Since r is close to 1it means that there is a strong positive relationship. Yes this is the sign we would expect to be associated with this coefficient. The percentage of the variation in the driving time to deliver a pizza explained by the number of miles for the trip is 87 87% HO:P^2=O H1:P^2=O r^2 Std. Err t Statistics t- value Decision Rule Decision

0.875825

0.029996988 31.198305 1.96 t < -1.96 or t>1.96 Reject Ho, Otherwise do not Reject Ho

Conclusion There is a significant linear relationship between the two variables

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Solution 2 Y(hat)=b0+b1(X) Y(hat)=1.0282+1.7496(X) Slope =1.7496

Slope tells us that average travel time will increase by 1.7496 for each additional 1 mile increase.

Solution 3 Y(hat)=b0+b1(X) Y(hat)=1.0282+1.7496(5)

9.7762

Solution 4 Regression Analysis Regression Statistics Multiple R 0.93585519 R Square 0.875824936 Adjusted R Square 0.875303192 Standard Error 0.669440371 Observations 240 ANOVA

Regression Residual Total

df 1 238 239

SS 752.287192 106.6597976 858.9469896

Intercept x (Distance)

Coefficients 1.028150902 1.749618857

Standard Error 0.171817273 0.042703504

MS 752.287192 0.44815041

F 1678.648897

Significance F 8.5472E-110

t Stat 5.983978717 40.97131798

P-value 7.94694E-09 8.5472E-110

Lower 95% 0.689674058 1.665493744

Upper 95% 1.366627746 1.833743969

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Confidence Interval Estimate Data X Value Confidence Level

5 95%

Intermediate Calculations Sample Size Degrees of Freedom t Value Sample Mean Sum of Squared Difference Standard Error of the Estimate h Statistic Average Predicted Y (YHat)

240 238 1.969981 3.894167 245.7518 0.66944 0.009143 9.776245

For Average Predicted Y (YHat) Interval Half Width Confidence Interval Lower Limit Confidence Interval Upper Limit For Individual Response Y Interval Half Width Prediction Interval Lower Limit Prediction Interval Upper Limit

0.126099 9.650146 9.902344

1.3248 8.451445 11.10105

Determination & Interpretation We are 95% confident that the values fall between (9.6501469.902344) and the prediction intervals associated with the pizza delivery that involved a five mile trip (8.451445 - 11.10105)

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14 SUMMARY OUTPUT Regression Statistics Multiple R 0.93585519 R Square 0.875824936 Adjusted R Square 0.875303192 Standard Error 0.669440371 Observations 240

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ANOVA df

SS

MS

F

Regression Residual Total

1 238 239

752.287192 106.6597976 858.9469896

752.287192 0.44815041

1678.648897

Significanc eF 8.5472E110

Intercept x (Distance)

Coefficients 1.0282 1.7496

Standard Error 0.1718 0.0427

t Stat 5.9840 40.9713

P-value 0.0000 0.0000

Lower 95% 0.6897 1.6655

Question # 5:

Upper 95% 1.3666 1.8337

Lower 99.0% 0.5820 1.6387

10 4

Upper 99.0% 1.4743 1.8605

The outliers are Distance 6.4 6.4

Travel time 12.55 12.58

From the scatter diagram we saw that these two sets of points are the outliers.

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