Reference no: EM132522341
A large national bank charges local companies for using their services. A bank official reported the results of a regression analysis designed to predict the bank's charges (Y), measured in dollars per month, for services rendered to local companies. One independent variable used to predict service charges to a company is the company's sales revenue (X), measured in millions of dollars. Data for all companies who use the bank'services were used to fit the model:
Yi = Bo + B1Xi +ei
The results of the simple linear regression are provided below:
Y hat = -2,7000 + 20x
a. Interpret the estimate of β0
b. Interpret the estimate of β1.
c. What does the regression predict to be the bank's charges per month, if the company's sales revenue is $200 million dollars?
d. The p-value for β1 is 0.034, what does this mean for the significance of β1?
An economist is interested to see how Consumption for an economy (in $ billions) is influenced by gross domestic product ($ billions) and aggregate price (consumer price index). The Excel output of this regression is partially reproduced below.
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.991
R Square 0.982
Adjusted R Square 0.976
Standard Error 0.299
Observations 10
ANOVA
df SS MS F Significance F
Regression 2 33.4163 16.7082 186.325 0.0001
Residual 7 0.6277 0.0897
Coeff StdError t Stat P-value
Intercept -0.0861 0.5674 -0.152 0.8837
GDP 0.7654 0.0574 13.340 0.0001
Price -0.0006 0.0028 -0.219 0.8330
a. What percentage of Consumption is explained by the regression? Explain.
b. Is this regression model significant? Explain.
c. Is the coefficient for GDP significant? Explain.
d. Is the coefficient for Price significant? Explain.
e. Use the model to predict the consumption level for an economy with GDP equal to $4 billlion and an aggregate price index of 150.
The managers of a brokerage firm are interested in finding out if the number of new clients a broker brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine the number of new clients they have enrolled in the last year and their sales amounts in thousands of dollars. These data are presented in the table that follows.
New
Broker Clients Sales
1 27 52
2 11 37
3 42 64
4 33 55
5 15 29
6 15 34
7 25 58
8 36 59
9 28 44
10 30 48
11 17 31
12 22 38
a. Set up a scatter plot with the dependent variable (Sales) on the vertical axis and independent variable (Clients) on the horizontal axis.
b. What is the least squares estimate of the slope from the regression?
c. Is the estimate of the slope significant at the 95% confidence level? Explain.
d. What does the slope estimate mean in relation to the problem facing the brokerage firm?
e. What is the regression estimate of the Y-intercept?
f. Is the estimate of the slope for the Y-intercept significant at the 95% confidence level? Explain.
g. What does the estimate of the Y-intercept mean in relation to the problem facing the brokerage firm?
h. How much in sales (in $1,000s) does the regression predict for a broker who brings 25 new clients into the firm?
i. What does the model predict for the case where the broker brings in 35 new clients?
j. What percentage of the total variation in sales generated can be explained by the number of new clients brought in?
A manager of a product sales group believes the number of sales made by an employee (Y) depends on how many years that employee has been with the company (X1) and how he/she scored on a business aptitude test (X2). She decides to perform a multiple linear regression to test this belief and use the resulting information for predicting sales. A random sample of 8 employees provides the following data:
Employee Y X1 X2
1 100 10 7
2 90 3 10
3 80 8 9
4 70 5 4
5 60 5 8
6 50 7 5
7 40 1 4
8 30 1 1
a. Perform a regression analysis on the data.
b. What is the adjusted r2 for this model?
c. What is the value for the three regression coefficients, b0, b1, and b2?
d. For each coefficient, determine whether it is significant at the 95% confidence level? Explain.
e. Using the regression model as estimated, if an employee who had been with the company 5 years scored a 9 on the aptitude test, what does the model predict for his or her expected sales?
f. residuals plot against the two independent variables and comment on your interpretation of the results.
The data below are quarterly revenues (in $millions) for Toys R Us from 1996-Q1 through 2015-Q1. (Data extracted from Standard & Poor's Stock Reports, November 1995, November 1998, and April 2002, and Toys R Us, Inc., www.toysrus.com.)
a. Do you think that the revenues for Toys R Us are subject to seasonal variation? Explain.
b. Plot the data. Does this chart support your answer in (a)?
c. Develop a linear trend forecasting equation with quarterly components.
e. Interpret the quarterly coefficients.
f. What are the forecasts for 2015-Q2, 2015-Q3, 2015-Q4, and all four quarters of 2016?
The data below are the annual milk production in gallons from a small dairy farm from 1984 to 2015.
a. line graph for milk production.
b. State the equation of a linear trend model for the data.
c. Run the linear trend regression.
d. Interpret the values of b0 and b1 resulting from the regression.
e. Is the model significant in predicting trend? Explain.
f. Predict milk production for 2016 and 2017.