Stat Facilitated Study Group (FSG)
14.10.2011
STAT FSG Times: Tuesdays 1 p.m to 2 p.m
Location: Room AC219
Fridays 11 a.m to 12 p.m
Location: Portable 04 Room 101
1. Make sure you know the meaning of:
a) Regression line
b) Residue
c) Correlation (r)
d) R square (R-sq)
e) Coefficient of determination (r◘)
f) Least-square regression line:
g)
h)
i)
j)
Why square? What is the sum and the mean of least-square residuals?
Extrapolation
Lurking variable
Why we can’t use a high correlation to conclude one variable is cause of the other?
2. Which statement about the below scatterplot is true:
a)
b)
c)
d)
It’s form is curved
It is right skewed
Correlation coefficient is negative
Correlation coefficient is 0.1
Stat Facilitated Study Group (FSG)
14.10.2011
STAT FSG Times: Tuesdays 1 p.m to 2 p.m
Location: Room AC219
Fridays 11 a.m to 12 p.m
Location: Portable 04 Room 101
3. A researcher expects a relationship between two variables, but finds that the correlation
between them is close to zero. The researcher has plenty of data. What is a possible
explanation?
(a) The relationship is a curve
(b) The relationship is strongly linear but the correlation happened to come out close to
zero.
(c) The relationship is a curved upward trend.
(d) There cannot actually be a relationship between the variables if the correlation is
close to zero.
4. A researcher studies children in school and finds a strong positive linear association
between height and reading ability. What would the researcher's best conclusion be?
(a) The observed association was an accident.
(b) In any grade, taller children are better readers.
(c) There is a lurking variable that explains the correlation.
(d) Height and reading ability are confounded.
5. You are given a set of data. Calculate the residue for X=3.
X … -1 3 6 …
Y … 0 12 24 …
Y=5x-10
6. The following statistical output was obtained from a regression analysis of the relationship between two variables x and y:
Regression Analysis: y versus x
The regression equation is y = 104 - 0.887 x
S = 1.56848
R-Sq = 27.0%
R-Sq(adj) = 26.2%
What is the correlation between x and y? Choose the closest value.
A) 0.27
B) -0.89
C) -0.27
D) 0.52
E) -0.52
Stat Facilitated Study Group (FSG)
14.10.2011
STAT FSG Times: Tuesdays 1 p.m to 2 p.m
Location: Room AC219
Fridays 11 a.m to 12 p.m
Location: Portable 04 Room 101
7. A researcher wishes to determine whether the rate of water flow (in liters per
second) over an experimental soil bed can be used to predict the amount of soil washed
away (in kilograms). The researcher measures the amount of soil washed away for
various flow rates, and from these data calculates the least-squares regression line to be
amount of eroded soil = 0.4 + 1.3 x ( flow rate).
What do we know about the correlation between amount of eroded soil and flow rate?
A) r = 1=1:3
B) r = 0:4
C) r = 1:3 � 0:4
D) It should be positive, but we cannot determine the exact value with the information given.
E) It should be negative, but we cannot determine the exact value with the information given.
8. One of the flow rates used by the researcher in question 24 above was 0.3 liters per
second and for this flow rate the amount of eroded soil was 0.8 kilograms. These values
were used in the calculation of the least-squares regression line shown in question 7.
What is the residual corresponding to these values?
A) 0.01
B) -0.01
C) 0.50
D) -0.50
E) 0.37