The table below reports data consisting of 30 observations. Each observation con
ID: 3262241 • Letter: T
Question
The table below reports data consisting of 30 observations. Each observation contains two values (one for Y and one for X). Please construct a linear regression of the structure: Y = a + bX.
What is the magnitude of the coefficient b in this model?
Question options:
5.630
3.035
0.998
20.442
Question 2
The table below consists of 30 observations where each observation includes two values (Y and X). Please estimate the following linear formulation using the table below:
Y = a + b X
and please use the estimated model to predict the value of Y when X is 50.
Question options:
157.37
155.25
158.39
151.95
Question 3
Please use the dataset from the table below to estimate the following linear regression model:
Y = a + b X
What is the residual for the very first observation in the dataset (Y=161, X=46)? Recall that the residual is the error, or the difference between the predicted value and the actual value.
Question options:
15.772
11.852
17.995
none of the above
The table below contains 30 observations, each containing Y and X values. Please estimate the following linear regression model on this dataset:
Y = a + b X
In this estimation, what is the level of statistical significance for the intercept coefficient (a) to be different from zero? I.e., the level of confidence above which, the test where the null hypothesis is that the coefficient (intercept) is equal to zero, fails to reject the null.
Question options:
0.42361
0.57639
0.5653
5.630
Including another independent variable into a regression model will always increase the adjusted R-square
Question options:
Question 1Explanation / Answer
Answer:
Question 1
The table below reports data consisting of 30 observations. Each observation contains two values (one for Y and one for X). Please construct a linear regression of the structure: Y = a + bX.
What is the magnitude of the coefficient b in this model?
a
5.630
Answer: b
3.035
c
0.998
d
20.442
Question 2
The table below consists of 30 observations where each observation includes two values (Y and X). Please estimate the following linear formulation using the table below:
Y = a + b X
and please use the estimated model to predict the value of Y when X is 50.
Question options:
Answer: a
157.37
b
155.25
c
158.39
d
151.95
Question 3
Please use the dataset from the table below to estimate the following linear regression model:
Y = a + b X
What is the residual for the very first observation in the dataset (Y=161, X=46)? Recall that the residual is the error, or the difference between the predicted value and the actual value.
Question options:
Answer: a
15.772
b
11.852
c
17.995
d
none of the above
Observation
Y
Predicted
Residual
1
161.0
145.2
15.8
The table below contains 30 observations, each containing Y and X values. Please estimate the following linear regression model on this dataset:
Y = a + b X
In this estimation, what is the level of statistical significance for the intercept coefficient (a) to be different from zero? I.e., the level of confidence above which, the test where the null hypothesis is that the coefficient (intercept) is equal to zero, fails to reject the null.
Question options:
a
0.42361
Answer: b
0.57639
c
0.5653
d
5.630
Question 5
Including another independent variable into a regression model will always increase the adjusted R-square
Question options:
a
True
Answer: b
False
Regression Analysis
r²
0.937
n
30
r
0.968
k
1
Std. Error
17.761
Dep. Var.
Y
ANOVA table
Source
SS
df
MS
F
p-value
Regression
131,820.5688
1
131,820.5688
417.87
2.29E-18
Residual
8,832.8979
28
315.4606
Total
140,653.4667
29
Regression output
confidence interval
variables
coefficients
std. error
t (df=28)
p-value
95% lower
95% upper
Intercept
5.6300
9.9598
0.565
.5764
-14.7717
26.0318
X
3.0347
0.1485
20.442
2.29E-18
2.7306
3.3388
Predicted values for: Y
95% Confidence Interval
95% Prediction Interval
X
Predicted
lower
upper
lower
upper
Leverage
50
157.367
149.569
165.165
120.158
194.575
0.046
Question 1
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