Regression Analysis, Confidence Interval & Moving Average

1. Sixto Sanchez is the owner of Suburban Stylists. He is evaluating the service level provided to walk-in customers. Because he is enrolled in an MBA program at Eastern University, Sixto decides to sample walk-in customers for the next two weeks. He collects information from 82 walk-in customers and calculates that their average waiting times that is 21 minutes with a standard deviation of 4 minutes.

a)Determine the degrees of freedom to be used in further analysis.
b)Calculate the two sided 95% confidence interval for the population mean of waiting times.
c)Calculate the two sided 90% confidence interval for the population mean of waiting times.
d)Calculate the two sided 99% confidence interval for the population mean of waiting times.
e)What t table value should be used in calculating a two sided 95% confidence interval for the population mean of waiting times if the sample selected is 25 instead of 82?

2. Bay Area Community College (BACC) has collected data comparing the starting salaries of their graduating students with last names beginning with the letters A through M with those whose last names begin with N through Z. The first category provided 47 random responses with an average starting salary of $29,426.42 and a standard deviation of $4,521.94. The second category had 52 random responses with an average starting salary of $22,863.81 and a standard deviation of $2,378.66.

a)If you assume that last names should not have an impact on starting salary of graduates of BACC, then what is the appropriate null hypothesis?
b)State the research hypothesis in words and in notation.
c)Calculate the appropriate test statistic.
d)Calculate the appropriate p-value for the test statistic.
e)Is the statistic statistically significant?
f)What type of error if any has been committed?

3. Plymouth Rock Securities is interested in finding out if there is a relationship between the number of new clients brought into the firm by a broker and the sales performance of the broker. A random sample of 11 brokers' records are reviewed to determine the number of new clients enrolled last year and total sales in millions of dollars:

Broker 1 2 3 4 5 6 7 8 9 10 11
Clients 27 11 42 33 15 15 25 36 28 30 17
Sales, $ 52 37 64 55 29 34 58 59 44 48 31

a)How closely related is the new client base to sales performance? Draw the scatterplot and compute the correlation and describe the relationship
b)Find the least-squares equation to predict sales from number of clients. Can the least squares equation be used to predict sales?
c)What does the slope represent?
d)What would a new broker who brings in 30 clients sell, on average?
e)How much of the variability in sales is not explained by the number of new clients?

4. Jean Siskel is an entertainment analyst for West Coast Securities. He is trying to develop a model to estimate gross earning generated by a new movie release. He has collected the following data on 20 movies: Gross Earnings, Production Costs, Promotion Costs, and if the movie is based on a bestseller novel:

Gross Earnings Production Cost Promotion Cost
Movie Millions $ Millions $ Millions $ Novel
1 28 4.2 1 0
2 35 6 3 1
3 50 5.5 6 1
4 20 3.3 1 0
5 75 12.5 11 1
6 60 9.6 8 1
7 15 2.5 0.5 0
8 72 10 12 1
9 45 6.4 8 1
10 37 7.5 5 0
11 30 5.0 1 1
12 63 10.1 10 0
13 58 7.8 9 1
14 50 6.9 10 0
15 24 3.5 4 0
16 82 11.0 15 1
17 48 10.7 1 1
18 34 6.6 2 0
19 50 8.4 3 1
20 45 10.8 5 0

a.What type of variable is novel?
b.What is the estimated multiple linear regression equation derived from this data?
c.What are the regression coefficients for each X variable? Interpret the regression coefficient.
d.Will Jean be pleased with the results?
e.Interpret the intercept value.

5. The following data represent revenues in thousands of dollars for a manufacturer of small electric appliances.
Year Quarter Revenues
1996 1 514
1996 2 822
1996 3 648
1996 4 976
1997 1 616
1997 2 884
1997 3 678
1997 4 996
1998 1 658
1998 2 850
1998 3 714
1998 4 1052

a)Calculate the moving averages for this time series.
b)Find the seasonal index for each quarter.
c)From the fourth quarter of 1997 to the first quarter of 1998, revenues declined. What happened on a seasonally adjusted basis?
d)Compute the forecast for the second quarter of 2002.
e)Find the regression equation to predict the long term trend in the seasonally adjusted revenues.