15) Consider the Midcity Pricing Structure case we discussed. We would like to study how the selling price of properties varies by neighborhood (recall that there were three neighborhoods). As such, the output from doing an ANOVA on the data set with respect to neighborhood yields the following:

ANOVA Summary
Total Sample Size 128
Grand Mean 130427.34
Pooled Std Dev 17863.20
Pooled Variance 319093956.08
Number of Samples 3
Confidence Level 95.00%

Price (1) Price (2) Price (3)
ANOVA Sample Stats Data Set #1 Data Set #1 Data Set #1
Sample Size 44 45 39
Sample Mean 110154.55 125231.11 159294.87
Sample Std Dev 15973.88 17866.05 19781.73
Sample Variance 255164862.58 319195828.28 391316815.11
Pooling Weight 0.3440 0.3520 0.3040

Sum of Degrees of Mean F-Ratio p-Value
OneWay ANOVA Table Squares Freedom Squares
Between Variation 51798469787.16 2 25899234893.58 81.16 < 0.0001
Within Variation 39886744509.71 125 319093956.08
Total Variation 91685214296.88 127

a) State explicitly (both using notation and words) the hypothesis that is being tested here, what the corresponding conclusion is, and why?

Now consider a regression model with Neighborhood as an independent variable and Price as dependent variable. Clearly, you will need to add dummy variables for the three neighborhoods. Assuming that the reference level that you use for the dummy variables is Neighborhood 2, the regression equation will be of the form

Where b0, b1, b2 are the regression coefficients, and Neighborhood1 is 1 for a property in neighborhood 1, 0 otherwise; and similarly, Neighborhood3 is 1 for a property in neighborhood 3, 0 otherwise.

b) What will be the estimates of the regression coefficients based on the ANOVA output shown above? Clearly explain the meaning of the coefficients. (Please note that if you answer this question by just running a new regression model, you are not answering the question the way I expect you to!)

c) What will the R-squared value of the regression model, again based on the ANOVA output shown above?

Solution Summary

Step by step method for computing regression model with dummy variables

First, explain in your own words (no direct quotes, please) what a dummyvariable is and its purpose in regression analysis. Secondly, provide an example of where you might use a dummyvariable from your own professional experience. Thirdly, briefly describe how you would implement a dummyvariable in a data table you intend to

When using dummyvariables in a regression equation to model a qualitative or categorical variable, the number of dummyvariables should equal to
a. one less than the number of categories.
b. one more than the number of categories.
c. the number of categories.
d. the number of other independent variables in the model

A county has four major hospitals: 1) Regional Memorial; 2) General; 3) Charity; and 4) City. A multiple regression model is used to compare the time spent in the hospital after a heart by-pass surgery among the four hospitals. The response (dependent) variable is the amount of time spent in the hospital (in days). The variables

1. Which of the following is a test of the statistical signficiance of the entire regression equation?
A. t-test
B. R2
C. F-test
D. Durbin-Watson
2. When the R2 of a regression equation is very high, it indicates that
A. all the coefficients are statistically signficant.
B.

Regression analysis was used to estimate the following seasonal forecasting equation:
St = 124 + 18 D1 - 46 D2 - 28 D3 + 2.5 t
D1 is a dummyvariable that is equal to one in the first quarter and zero otherwise; D2 is a dummyvariable that is equal to one in the second quarter and zero otherwise; and D3 is a dummyvariable

Please reference attachments to answer the following:
Choose Data1 or Data2, and work the following problems:
The number of dummyvariables is the number of levels of the categorical variable less one because the one left out is quantified by the intercept. Each coefficient of the dummyvariables effects a shift in the in

Consider the following time series data representing quarterly sales of dishwashers at Big Boys Appliances over the past two years:
Time Sales
2010 Quarter 1 20
2010 Quarter 2 85
2010 Quarter 3 64
2010 Quarter 4 30
2011 Quarter 1 70
2011 Quarter 2 125
2011 Quarter 3 105
2011 Quarter 4 90
The scatter plot of the da

Discussion of multiple regression with the topics from Dielman Terry 'Applied Regression Analysis' - A 2nd course in Bus. and Economic Statistics.
Topics (title of chapters) to cover:
- Multiple regression analysis
- Fitting curves to data
- Assessing the assumptions of the regression model
- Using indicator and interact

A. What does R squared measure in a simple regression, in a multiple regression?
b. What is the purpose of the F test in a multiple regression?
c. What is a qualitative independent variable? How would we/what technique would we use to include a qualitative independent variable in a regression model.