PUPPALA KARTIK STARBUCKS INTRODUCES DEBIT CARD SECTION B

1) Here, dependent variable, y = Amount of Prepaid Card ($)Ind. variables, x1 = Age, x2 = Days spent/month , x3 = Cups/day, x4 = Income ($1000)

Regression Statistics Coeff t Stat P-valueMultiple R 0.868700283 Intercept -83.8257 -3.72651 0.001332R Square 0.754640181 X Var 1 0.236929 0.411402 0.685153Adjusted R Square 0.705568218 X Var 2 1.189657 0.80713 0.429086Standard Error 22.14831563 X Var 3 1.421611 0.540321 0.594942Observations 25 X Var 4 2.406543 6.690062 1.64E-06

The regression equation is: ŷ = -83.826 + 0.237x1 + 1.189x2 + 1.421x3 + 2.406x4

F value is 15.378, with p = 6.76E-06, meaning the model adds good predictability. R2 is 0.7546 and adjusted R2 is 0.7055, so R2 is inflated by only 4.81% and 70.55% of the variance of Card Amount can be explained by the model, which is high, so the model is quite good.

The t-statistic is significant only for variable x4 (6.69) with an associated p value of 1.64E-06. For other variables, p value is high, so only income acts as a good predictor for Card Amount.

2) Here, dependent variable, y = Days spent/month at StarbucksIndependent variables, x1 = Age, x2 = Cups of coffee/day, x3 = Income ($1000)

Regression Statistics Coeff t Stat P-valueMultiple R 0.640512 Intercept -0.97851 -0.52795 0.603068R Square 0.410256 X Var 1 0.068746 1.515961 0.144438Adjusted R Square 0.326007 X Var 2 0.334046 3.403894 0.002674Observations 25 X Var 3 -0.01155 -0.38867 0.701434

The regression equation is: ŷ = -0.97851 + 0.069x1 + 0.334x2 – 0.012x3

F value is 4.87, with p = 0.01, meaning the model adds predictability only for > 0.01. R2 is 0.41 and adjusted R2 is 0.326, so R2 is inflated by 7.40% and only 32.60% of the variance of Days spent can be explained by the model, so the model is not very good.

The t-statistic is significant only for variable x2 (3.404) with an associated p value of 0.00267. For other variables, p value is high, so only age acts as good predictor for Days spent/month.

3) Here, dependent variable, y = Sales RevenueIndependent variables, x1 = No. of stores, x2 = No. of drinks, x3 = Avg. weekly earnings

The regression equation is: ŷ = -13500.2 - 0.026x1 – 75.2x2 + 38.99x3

F value is 4539.2, with p = 5.5E-06 so the model adds considerable predictability. R2 is 0.9998 and adjusted R2 is 0.9995 which are almost similar. So 99.95% of the variance of Sales can be explained by the model, so the model is excellent.

The t-statistic is significant for variables x2 (-7.468) and x3 (38.98) but not so much for x2 (-0.9517), so No. of drinks and Avg. weekly earnings act as good predictors for total Sales Revenue.

PUPPALA KARTIK VIRGINIA SEMICONDUCTOR SECTION B

1) We use Stepwise Regression here. After 1st step, Company Size is the best predictor with the highest t-value (5.64). After 2nd step, central purchasing is added to the model. Even though the coefficient for x1 is small, we don’t ignore it as its unit is million. In the next step, no significant t-value is seen, so there are only 2 predictors in the model.

Regression Statistics Coefficients t Stat P-valueMultiple R 0.877506 Intercept -7.77108 -0.19801 0.846097R Square 0.770017 Size (x1) 1.450821 4.26348 0.000924Adjusted R2 0.734635 Purch. (x4) 109.407 2.067435 0.059204Standard Error 87.39594 df F Significance Observations 16 Regression 2 21.76295 7.1E-05

The multiple regression model is: ŷ = -7.77 + 1.45x1 + 109.407x4

F is 21.763, which is high and the R2 (0.77) as well as adjusted R2 (0.734) values are quite high so the model is quite strong. The Company Size ($ million sales) is the most important predictor variable while central purchasing agent also plays an important role.

2) Stepwise regression shows that neither predictor has significant t-value. A scatter plot for hours (x1) and number of customers (x2) are close to lower left and upper left quadrants of Tukey’s approach respectively. So new variables recoded are log(x) and -1/sqrt(x).

Stepwise regression gives the model: ŷ = 497.22 – 61.25/sqrt(x2) + 5.6x1 – 436.9log(x1)F is 12.28 while the R2 and adjusted R2 are 0.84 and 0.77 respectively, which means the model is pretty good. The first two variables in model are significant predictors with p-values 0.003 and 0.034 respectively.

3) The scatter chart is same as upper left quadrant of Tukey so we consider logx and -1/sqrtx

The regression equation is: ŷ = 30148.68 – 11275.6log(x) - 85605.8/sqrt(x) + 9.43x

Coeff t Stat P-valueIntercept 30148.68 5.804087 0.001147log (x) -11275.6 -5.71603 0.001242-1/sqrt (x) 85605.8 5.974743 0.000986No. of Emp 9.429008 5.268947 0.001885

F is 127.8 while R2 and adjusted R2 are 0.984 and 0.976 respectively which mean the model is very good. In the 1st step, -1/sqrt(x) enters the model, in the 2nd step, log(x) enters while in the final step, x enters the model.