# Multiple Regression Analysis & Probability

See attached template file.

28. Suppose the regional express delivery service wants to estimate the cost of shipping a package (y) as a function of cargo type, where cargo type includes the following possibilities: fragile, semi fragile, and durable. Costs for 15 randomly chose packages od approximately the same weight and same distance shipped, but of different cargo types are provided in the excel sheet titled ( prob 28)

a. Formulate a multiple regression model to predict the costs of shipping a given package

b. Estimate the formulated model using the given sample data, and interpret the estimated regression coefficients.

c. According to the estimated regression model, which cargo type is the least costly to ship?

d. How well does the estimated model fit the given sample data? How can the models goodness of fit be improved?

e. Given the estimated regression model, predict the cost of shipping a package with semi fragile cargo

4. Suppose that 18% of employees at a given cooperation engage in physical exercise activities during the lunch hour. More over assume that 57% of all employees are male and 12% of all employees are males who engage in physical activities during the lunch hour.

a. If we chose an employee at random from this cooperation, what is the probability that this person is a female who engages in physical exercise activities during the lunch hour?

b. If we chose an employee at random from this corporation, what is the probability that this person is a female who DOES NOT engage in physical activity during lunch hour.

12. A study has shown that the probability distribution of X, the number of customers in line (including the one being served if any)at a checkout counter in a dept. store is given by P(X=0) =0.25, P (X=1) = 0.25, P (X=2) = 0.20, P= (x=3) =0.20, and P (x≥4)= 0.10. Consider a newly arriving customer to the checkout line.

a. What is the probability that the customer will not have to wait behind anyone?

b. What is the probability that this customer will have to wait behind at least one customer?

c. On average, behind how many other customers will the newly arriving customer have to wait?

2. Suppose that it is known that the distribution of purchase amounts by customers entering a popular retail store is approximately normal with mean $25 and standard deviation $8.

a. What is the probability that a randomly selected customer spends less than $35 in the store?

b. What is the probability that a randomly selected customer spends between 15- $35 in the store?

c. What is the probability that a randomly selected customer spends more than $10 at this store?

d. Find the dollar amount such that %75 of all customers spend at least this amount.

e. Find the dollar amount such that %80 of all customers spend at least this amount.

f. Find two dollar amounts, equidistant from the mean of $25, such that 90% of all customer purchases are between these values.

#### Solution Summary

The solution provides step by step method for the calculation of multiple regression model and probability. Formula for the calculation and Interpretations of the results are also included.