STAT 2112 GWU Statistics Null Hypothesis & Regression Model Questions

STAT2112.10 Quiz # 4 NAME:__________________GWID:G________________Fall 2022
sba
Takehome Due 7:25pm,Monday (11/14)
1. In a multiple regression study with 60 observations, an analyst is considering whether or not
to add a fourth predictor to variable. The SSE of the model when the fourth variable is included
is 28,422. The SSE of the model when the fourth variable is not included is 30,224. Based on the
partial F-statistic of ___________ we would conclude that at α=0.05, the additional variable
____________ the model.
A. 3.49; does not significantly improve
B. 5.35; significantly improves
C. 1.74; does not significantly improve
D. 2.38; does not significantly improve
E. None of the above — write your own correct answer:___________,____________
2-3 Match the statements below with the corresponding terms from the list. (a correct match gets
1/6 of one point)
a) multicollinearity
b) extrapolation
c) R2a adjusted
d) quadratic regression
e) interaction
f) residual plots
g) Parsimony principle
h) dummy variables
i) cause and effect
j) VIF (variance inflation factor)
2
k) R
l) residual
m) influential points
n) outliers
o) Parsimony principle
p) homoscedasticity of variance
q) heteroscedasticity
r) PRESS statistics
____ Used when a numerical predictor has a curvilinear relationship with the response.
____ Worst kind of outlier, can totally reverse the direction of association between x and y.
____ Used to check the assumptions of the regression model.
____ Used when trying to decide between two models with different numbers of predictors.
____ Used when the effect of a predictor on the response depends on other predictors.
____ Proportion of the variability in y explained by the regression model.
____ Is the observed value of y minus the predicted value of y for the observed x.
____ A point that lies far away from the rest.
___ is a form of cross-validation used in regression analysis to provide a summary measure of
the fit of a model to a sample of observations that were not themselves used to estimate the
model.
____ Can give bad predictions if the conditions do not hold outside the observed range of x’s.
____ Can be erroneously assumed in an observational study.
____ is a measure of collinearity/multi-collinearity.
____is the principle that the simplest explanation that can explain the data is to be preferred.
____ is an assumption of equal or similar variances in different groups being compared.
____ refers to situations where the variance of the residuals is unequal over a range of measured
values.
____ Problem that can occur when the information provided by several predictors overlaps.
____ Used in a regression model to represent categorical variables.
4-7 For a study of crime in the United States, data for each of the 50 states and Washington, DC
was collected on the violent crime rate (per 100,000 citizens), poverty rate (percent of the
population), single parent households (percent of all state households), and urbanization (percent
of state population living in urban areas). Parts of the relevant analysis are provided below:
Table 1
CV
Regression
df
?
SS
2082535.14
.
Error/Residual
Total
?
?
?
2913657.92
.
And
Table 2
Intercept
Poverty rate
Single parent rate
Urbanization rate
Coefficients
-786.75
13.40
33.02
4.40
Standard Error
116.42
7.60
5.52
0.99
4. Write the null hypothesis and complete Table 1 (make sure to compute the F-statistics).
5. Are there sufficient evidence to Reject the null hypotheses at α=0.05? What are the R2 and
Adjusted R2a ?
6. Write the fitted regression model and based on the relevant evidence order the predictors with
the one that has the strongest impact on the violent crime (rate).
7. In a multiple regression model with n=100; k=6, SSTOT = 200 and SSE = 50. The adjusted
coefficient of determination (Adjusted R2) is:_____________
The F-Statistics is:_____________________
Questions 8-9 are based on the following facts.
Suppose you got a job offer from the DC Police Department. Your first assignment is to survey
100 seniors at GWU and collect the following information.
1. percent alcohol in blood
2. number of drinks consumed
3. weight
4. sex (male or female)
5. Race (While, African American, Spanish, Other)
6. average time (hour) spent in consuming drinks in a week.
8. Propose and write a complete model that might be used to predict the % alcohol in blood level.
Additional information for question 9. You performed the multiple linear regression analysis on
the full model you identified in question 8 and obtained SSE=4960. The chief of police wants
you to test whether Sex and Race have any associations with the %alcohol level. So, you
analyzed the data again after removing these variables and obtained SSE=5877.
9. Using the additional information provided above, write the null hypothesis and test that
hypothesis at 0.05 level.
10. We collected data on hospital stay on 100 Covid-19 patients who were admitted to ICU at
Washington Hospital. Length of stay (day) was the dependent variable and we have data on 9
predictors (independent variables). Data was analyzed using multiple linear regression and
obtained F-statistics=14.78.
a. Test the global null and state your result and conclusion at 0.05 level
b. Compute R2
c. Compute Adjusted R2a