Homework 10
docx
keyboard_arrow_up
School
New Mexico State University *
*We aren’t endorsed by this school
Course
544
Subject
Political Science
Date
Apr 3, 2024
Type
docx
Pages
4
Uploaded by ProfHeatFox16
POLS 544: Public Policy Analysis
Homework 1, Introduction and Assumptions of Regression Analysis
Please type your answers into this Word document and upload onto Canvas. Answers in single-
space. (Total 20 points)
Part 1. Please provide your answers in one or two sentences. (16 points)
1. The following are four major assumptions required for regression analysis. In one or two
sentences, first define each concept. Then, explain its importance for regression interpretation.
1) Correctly specified model: (2 points)
Answer
: A correctly specified model is said to be correctly specified when
the model includes all relevant variables and relationships among those variables without including unnecessary or irrelevant variables.
2) Linearity: (2 points)
Answer
: Linearity of the relationship between dependent and independent variables :
3) Multicollinearity: (2 points)
Answer
: Multicollinearity occurs when two or more independent variables
in a regression model are significantly correlated with one another. It is a statistical phenomena that can interfere with the estimation and interpretation of regression coefficients.
4) Homoscedastic (or random) distribution of errors: (2 points)
Answer
: this is a circumstance in which the variance of a regression model's residual or error term remains constant. In other words, the error term remains constant as the value of the predictor variable changes. This suggests that the variance of all data points is nearly the same.
2. Model Specification: When setting up a regression model, why is it important to include more
than one independent variable? Conversely, what is the problem of having too many
independent variables? Provide both statistical (technical) and substantive reasoning. (2
points)
Answe
r
: Examine complex relationships: Multiple independent variables allow you to examine more complex relationships and interactions between variables. For example, the effect of one independent variable on the dependent variable might depend 1
on the level of another independent variable.
Problem; Multicollinearity occurs when two or more independent
variables are highly correlated, making it difficult to discern the effect of each variable separately. This can result in unstable estimates and inflated standard errors.
3. Goodness-of-Fit
1) Statistically significance of the unstandardized B coefficients are not enough to determine
the utility of a regression line. In one or two sentences, define “Goodness of Fit” for a
regression line and explain its importance. (2 points)
Answer
: The goodness of fit in regression refers to how well a regression
model matches the observed data. It assesses the degree to which the projected values from the regression line match the actual observed values.
The goodness of fit determines whether the regression model's assumptions are met. These assumptions include linearity, error independence, constant error variance (homoscedasticity), and error normality.
2) In one or two sentences, define and explain the following two measures of goodness-of-fit:
a. “Standard error of the estimate” (2 points)
Answer
: The standard error of the estimate measures the accuracy of a regression model's predictions. It calculates the average deviation of the observed values from the expected values using
the regression line.It helps us to determine the overall accuracy of the regression model.
b. “Coefficient of determination (or R
2
value)” (2 points)
Answer
: This is a statistical measure that represents the proportion of the variance for a dependent variable that's explained by an independent variable or variables in a regression model.
A higher
R-squared value suggests that the model is a better fit for the data. R-squared enables researchers to assess multiple models and choose the one that best explains the variation in the dependent variable.
Part 2. Regression equation (4 points)
2
You hypothesize that public agencies that have more interest groups testifying on their behalf
are more likely to receive greater budget appropriations the following fiscal year. To explore
this question, you collect the following data. - Y (dependent variable): Percentage increase in the amount of appropriations
- X (independent variable): Number of interest groups testifying on behalf of that agency Xi: (independent) Number of interest
groups testifying
Yi: (dependent)
Percentage increase
in appropriations
Agency 1
22
25
Agency 2
14
17
Agency 3
7
8
Agency 4
18
19
Agency 5
10
12
1) Using the data above, calculate and identify the regression equation (up to two decimal
points). * No need to conduct any hand calculations. Use the Excel file
available on Canvas modules to
derive the regression equation. Input the numbers above into the appropriate box. Please
reupload the completed excel file onto Canvas.
(MBB p. 332-333 contains more information on
calculation procedures).
(2 points)
Answe
r
: (should assume format Ŷ = α + β*Xi)
standard error of the estimate
2) Provide both a technical (a one unit change in IV predicts a X unit change in DV) and
substantive interpretation (what are the policy implications?). (2 points)
Answer
:
If the IV represents a person's number of years of schooling and the DV reflects their income, a technical interpretation of t
he slope coefficient could be that every additional year of education results in an average change in income of 1.08 units. or it could be that one year of further schooling is connected with an average
rise in income of 1.08 units. This implies that education has an important role in determining income levels, and policymakers may focus on improving educational opportunities to improve economic outcomes.
* Please upload BOTH this word document and the excel file (used to calculate the
regression equation in Part 2) onto Canvas. 3
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
4