# Business Case on Pronto Pizza

July 10, 2017 | Author: Muhammad Bilal | Category: Errors And Residuals, Statistical Theory, Statistical Inference, Statistics, Estimation Theory

#### Description

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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