Purpose Statement and Model 1 In the introductory paragraph

Purpose Statement and Model

1) In the introductory paragraph, state why the dependent variable has been chosen for analysis. Then make a general statement about the model:

“The dependent variable _______ is determined by variables ________, ________, ________, and ________.”

2) In the second paragraph, identify the primary independent variable and defend why it is important.

“The most important variable in this analysis is ________ because _________.” In this paragraph, cite and discuss the two research sources that support the thesis, i.e., the model.

3) Write the general form of the regression model (less intercept and coefficients), with the variables named appropriately so reader can identify each variable at a glance:

Dep_Var = Ind_Var_1 + Ind_Var_2 + Ind_Var_3

For instance, a typical model would be written:

Price_of_Home = Square_Footage + Number_Bedrooms + Lot_Size

Where

Price_of_Home: brief definition of dependent variable

Square_Footage: brief definition of first independent variable

Number_Bedrooms: brief definition of second independent variable

Lot_Size: brief definition of third independent variable

[Note: student of course replaces these variable names with his/her own variable names.]

Definition of Variables

4) Define and defend all variables, including the dependent variable, in a single paragraph for each variable. Also, state the expectations for each independent variable. These paragraphs should be in numerical order, i.e., dependent variable, X1, then X2, etc.

In each paragraph, the following should be addressed:

How is the variable defined in the data source?

Which unit of measurement is used?

For the independent variables: why does the variable determine Y?

What sign is expected for the independent variable\'s coefficient, positive or negative? Why?

Data Description

5) In one paragraph, describe the data and identify the data sources.

From which general sources and from which specific tables are the data taken? (Citing a website is not acceptable.)

Which year or years were the data collected?

Are there any data limitations?

Presentation and Interpretation of Results

6) Write the regression (prediction) equation:

Dep_Var = Intercept + c1 * Ind_Var_1 + c2 * Ind_Var_2 + c3* Ind_Var_3

7) Identify and interpret the adjusted R2 (one paragraph):

Define “adjusted R2.”

What does the value of the adjusted R2 reveal about the model?

If the adjusted R2 is low, how has the choice of independent variables created this result?

8) Identify and interpret the F test (one paragraph):

Using the p-value approach, is the null hypothesis for the F test rejected or not rejected? Why or why not?

Interpret the implications of these findings for the model.

9) Identify and interpret the t tests for each of the coefficients (one separate paragraph for each variable, in numerical order):

Are the signs of the coefficients as expected? If not, why not?

For each of the coefficients, interpret the numerical value.

Using the p-value approach, is the null hypothesis for the t test rejected or not rejected for each coefficient? Why or why not?

Interpret the implications of these findings for the variable.

Identify the variable with the greatest significance.

10) Analyze multicollinearity of the independent variables (one paragraph):

Generate the correlation matrix.

Define multicollinearity.

Are any of the independent variables highly correlated with each other? If so, identify the variables and explain why they are correlated.

State the implications of multicollinearity (if found) for the model.

11) Other (not required):

If any additional techniques for improving results are employed, discuss these at the end of the paper

Team	Seating Capacity	Salary ($)	Salary ($M)	Batting	ERA	HR	Error	Stolen Bases	Wins	Attendance
Boston	33,871	123,505,125	123.5	0.281	4.74	199	109	45	95.0	2,847,798
New York Yankees	57,746	208,306,817	208.3	0.276	4.52	229	95	84	95.0	4,090,440
Oakland	43,662	55,425,762	55.4	0.262	3.69	155	88	31	88.0	2,108,818
Baltimore	48,262	73,914,333	73.9	0.269	4.56	189	107	83	74.0	2,623,904
Los Angles Angels	45,050	97,725,322	97.7	0.270	3.68	147	87	161	95.0	3,404,636
Cleveland	43,368	41,502,500	41.5	0.271	3.61	207	106	62	93.0	2,014,220
Chicago White Sox	44,321	75,178,000	75.2	0.262	3.61	200	94	137	99.0	2,342,804
Toronto	50,516	45,719,500	45.7	0.265	4.06	136	95	72	80.0	2,014,995
Minnesota	48,678	56,186,000	56.2	0.259	3.71	134	102	102	83.0	2,034,243
Tampa Bay	44,027	29,679,067	29.7	0.274	5.39	157	124	151	67.0	1,141,915
Texas	52,000	55,849,000	55.8	0.267	4.96	260	108	67	79.0	2,525,259
Detroit	40,000	69,092,000	69.1	0.272	4.51	168	110	66	71.0	2,024,505
Seattle	45,611	87,754,334	87.8	0.256	4.49	130	86	102	69.0	2,724,859
Kansas City	40,529	36,881,000	36.9	0.263	5.49	126	125	53	56.0	1,371,181
Atlanta	50,062	86,457,302	86.5	0.265	3.98	184	86	92	90.0	2,520,904
Arizona	49,075	62,329,166	62.3	0.256	4.84	191	94	67	77.0	2,059,327
Houston	42,000	76,799,000	76.8	0.256	3.51	161	89	115	89.0	2,805,060
Cincinnati	42,059	61,892,583	61.9	0.261	5.15	222	104	72	73.0	1,923,254
New York Mets	55,775	101,305,821	101.3	0.258	3.76	175	106	153	83.0	2,827,549
Pittsburgh	38,127	38,133,000	38.1	0.259	4.42	139	117	73	67.0	1,817,245
Los Angeles Dodgers	56,000	83,039,000	83.0	0.253	4.38	149	106	58	71.0	3,603,680
San Diego	42,445	63,290,833	63.3	0.257	4.13	130	109	99	82.0	2,869,787
Washington	56,000	48,581,500	48.6	0.252	3.87	117	92	45	81.0	2,730,352
San Francisco	40,800	90,199,500	90.2	0.261	4.33	128	90	71	75.0	3,181,020
St Louis	49,625	92,106,833	92.1	0.270	3.49	170	100	83	100.0	3,542,271
Florida	42,531	60,408,834	60.4	0.272	4.16	128	103	96	83.0	1,852,608
Philadelphia	43,500	95,522,000	95.5	0.270	4.21	167	90	116	88.0	2,665,304
Milwaukee	42,400	39,934,833	39.9	0.259	3.97	175	119	79	81.0	2,211,323
Chicago Cubs	38,957	87,032,933	87.0	0.270	4.19	194	101	65	79.0	3,100,092
Colorado	50,381	48,155,000	48.2	0.267	5.13	150	118	65	67.0	1,914,385

Solution