Question 1 Uber has become extremely popular as an alternate, efficient means of

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Question 1 Uber has become extremely popular as an alternate, efficient means of transportation across the g lobe. An Uber customer place s an order, which then gets assigned to a nearby Uber driver. The customer and the driver exchange no cash or other form of payment-the cost of the ride in automatically charged to the customer's predetermined credit or debit card. Gratuity is authorized by the customer at the end of the ride and is at the customer's sole discretion. A new Uber driver wants to estimate the amount of tips he could earn based on the fare charged by Uber. The driver randomly samples five recent rides given by his colleagues. The data is shown below Fare S13 S26 Ti $5.00 $6.00 $4.00 S5.50 $3.00 $16 S22 $9 a. Calculate the regression coefficients and write out the regression model in good form. b. Use the model calculated in part (a) to estimate a tip on a $19 fare. Calculate the coefficient of determination and comment on its meaning in the context of this scenario. Test the Tip variable for significance in the model. Use the critical value approach at the O.05 C. d. level of significance. e. Test the model for overall significance, using the critical and p-value approaches at the 0.05 level of significance.

Explanation / Answer

a)

y=2.048+0.1542*fare

b)

y=2.048+0.1542*19

y=4.9775 = 4.98

c)

r^2=0.76556154 which means that 76.56% of the variation in dependent variable is accounted for by the independent variable.

d)

t=r*sqrt(n-2/1-r2)

                         =0.875*sqrt(5-2/1-0.7656)

                         =0.875*3.58

                         =3.13

t critical value with 15 degrees of freedom and significance level=0.05=2.35

We observe only t = 3.13

It lies below the critical t of 2.35

So the null hypothesis of no relationship in the population (r = 0) should be rejected

e)

Significance F is 0.0520 which is greater than a=0.05 and hence the model is significant- cannot reject the null hypothesis

SUMMARY OUTPUT Regression Statistics Multiple R 0.874963739 R Square 0.765561545 Adjusted R Square 0.687415393 Standard Error 0.673236719 Observations 5 ANOVA df SS MS F Significance F Regression 1 4.440256959 4.440256959 9.796535433 0.052067902 Residual 3 1.359743041 0.45324768 Total 4 5.8 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 2.048179872 0.899149393 2.277908307 0.107141397 -0.813314792 4.909674535 Fare 0.154175589 0.049258293 3.129941762 0.052067902 -0.002586284 0.310937462

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