Correlation & Regression Analysis – Quiz
1) What is the mathematical equation of a straight line?
2) The “best-fitting” straight line in a plot of dependent variable Y versus independent variable X is
the line that minimizes the sum of squares of the deviations of the observed values of Y from the
predicted values. This line is called?
3) Real data almost never fall exactly on a straight line. The differences between the values of the
responses obtained and the values given by the regression model are called?
4) A statistic used in simple linear regression that measures the strength of the linear relation that
exist between two variables (or a piece of information that gives us a measure for the type of fit that
exists between the straight line and the data).
5) In simple linear regression r = - 0.9 indicates?
6) Explained Variation is defined by?
7) Unexplained Variation is?
8) Total Variation is?
9) The Explained Variation divided by the Total Variation is called?
10)
1−
UnExplained Variation
=?
Total Variation
11) A statistic that gives us a method of measuring the effectiveness of ANY prediction model.
12) If errors are not independent we get error terms that may be correlated over time and are said to
be?
13) In multiple regression at least one dependent and two or more independent variables are
involved. A second-order linear model with two predictor values would be defined by?
14) If the value of one statistical error does not depend on the value of any other error we say that
the errors are?
15) Data that does not fall on a straight line will always give an r-value between?
16) An r-value in simple linear regression is close to zero. What does it mean?
17) How does extending a regression line beyond its range of relevancy affect the accuracy of the
regression model?
18) A statistical test for determining if there is an autocorrelation is called?
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19) The Y-intercept â is equal to?
20) Regression coefficient b̂ (or slope) is equal to?
21) A statistic used in regression analysis to test the hypothesis that there is no relationship between
X and Y.
Six groups of people were put on a diet and exercise plan. Estimate the regression for the
relationship between the average numbers of pounds of weight lost of each group and the number of
weeks each of the groups was on the plan. The quantitative relationship between the number of
weeks a group participated and the average number of pounds lost is shown below. Determine the
Least Squares regression line relating average weight loss to the number of weeks on the plan.
Accumulated Data
Group
A
B
C
D
E
F
X
1
3
6
2
5
4
# of weeks participated (X)
1
3
6
2
5
4
Y
2
6
11
6
11
8
X2
Pounds of weight lost (Y)
2
6
11
6
11
8
Y2
XY
22) Calculate the slope bˆ
23) Calculate the Y-intercept â
24) On average how many weeks should one participate in the plan to expect to lose 20 pounds?
25) Calculate the correlation coefficient.
26) How much variation in average weight loss can be explained by diet plus exercise?
Answers:
A1) 1.55
A2) 1.77
B) Lack-of-fit errors
C)
n ∑ X i Yi − (∑ X i )(∑ Yi )
 n (X 2 ) − ( X )2   n (Y 2 ) − ( Y )2 
∑ i   ∑ i ∑ i 
 ∑ i
D) Correlation Coefficient
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E)
n ∑ X i Yi − (∑ X i )(∑ Yi )
n∑ X 2i − (∑ X i )
2
=
∑(X i Yi ) − n(X )(Y )
F1) Low Positive Correlation
(
ˆ −Y
G1) ∑ Y
i
)
2
∑ X i2 − n(X )
2
F2) High Negative Correlation
b
G2)




S XY
∑X
2
− n(X )
2




H) Total Variation–Explained Variation
I) Y = β0 + β1X
J1) 89 %
J2) 92.5 %
K1) Coefficient of Determination
K2) Effectiveness Ratio
L) y = β0 + β1x1 + β2x2 + β3x1x2 + β4(x1)2 + β5(x2)2 + ε
M1) Serially Correlated
M2) Time Correlated
N) Y − bˆ X
O1) 1.902
O2) 1.135
P1) Auto-correlation Test
P2) Dubin-Watson Test
Q) r2
R) ∑ Yi − Ŷ
S1) Least Squares Line
S2) Regression Line
T1) 0.962
T2) 0.943
U1) Uncorrelated
U2) Independent
V1) -1 and +1
V2) 0 and +1
(
)
2
W) ∑(Yi − Y )
2
X1) There is no relationship between the two variables.
X2) A linear relationship does not exist between the two variables.
Y1) Negatively
Y2) Positively
Z1) 10.7
Z2) 11.8
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