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13
 
 
 
 
 
 
 
 
 
 
14
 
 
 
 
 
 
 
 
 
 
15
 
 
 
PAY ATTENTION
 
 
 
16
 
 
 
 
 
 
17
 
 
 
 
 
 
 
 
 
 
18
 
 
 
 
 
 
 
 
 
 
19
 
 
 
 
 
 
 
 
 
 
20
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Given are five observations for two variables, x and y.
 
 
 
 
 
 
 
x
y
 
 
 
 
 
 
 
 
 
1
3
 
 
 
 
 
 
 
 
 
2
8
 
 
 
 
 
 
 
 
 
3
6
 
 
 
 
 
 
 
 
 
4
11
 
 
 
 
 
 
 
 
 
5
16
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
The predicted value of y when x = 4 is:
 
 
 
 
 
 
a
 
9.6
 
 
 
 
 
 
 
 
b
 
10.6
 
 
 
 
 
 
 
 
c
 
11.7
 
 
 
 
 
 
 
 
d
 
12.2
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
2
The standard error of estimate for the model is:
 
 
 
 
 
a
2.214
 
 
 
 
 
 
 
 
 
b
2.033
 
 
 
 
 
 
 
 
 
c
1.949
 
 
 
 
 
 
 
 
 
d
1.822
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
3
The percent of variations in y explained by the variations in x is:
 
 
 
 
a
59.4%
 
 
 
 
 
 
 
 
 
b
68.1%
 
 
 
 
 
 
 
 
 
c
76.2%
 
 
 
 
 
 
 
 
 
d
85.1%
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Next FOUR questions are based on the following
 
 
 
 
 
 
How much does education affect wage rates?  Use the following data to develop an estimated regression equation that could be used to predict the WAGE for a given number of years of education.
 
 
 
y
x
 
 
 
 
 
 
 
 
 
WAGE
EDUC
 
 
 
 
 
 
 
 
 
18.70
16
 
 
 
 
 
 
 
 
 
11.50
12
 
 
 
 
 
 
 
 
 
15.04
16
 
 
 
 
 
 
 
 
 
25.95
14
 
 
 
 
 
 
 
 
 
24.03
12
 
 
 
 
 
 
 
 
 
20.00
12
 
 
 
 
 
 
 
 
 
53.84
16
 
 
 
 
 
 
 
 
 
25.00
12
 
 
 
 
 
 
 
 
 
28.85
16
 
 
 
 
 
 
 
 
 
16.83
13
 
 
 
 
 
 
 
 
 
14.80
12
 
 
 
 
 
 
 
 
 
43.25
16
 
 
 
 
 
 
 
 
 
19.23
12
 
 
 
 
 
 
 
 
 
14.00
14
 
 
 
 
 
 
 
 
 
8.00
12
 
 
 
 
 
 
 
 
 
57.70
21
 
 
 
 
 
 
 
 
 
20.00
12
 
 
 
 
 
 
 
 
 
20.83
18
 
 
 
 
 
 
 
 
 
22.00
11
 
 
 
 
 
 
 
 
 
68.75
14
 
 
 
 
 
 
 
 
 
10.50
12
 
 
 
 
 
 
 
 
 
9.88
13
 
 
 
 
 
 
 
 
 
10.96
12
 
 
 
 
 
 
 
 
 
8.25
13
 
 
 
 
 
 
 
 
 
14.86
18
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
4
The numerator of the formula to compute the slope coefficient of the regression equation is ________.
 
 
Use Excel!!
 
 
 
 
 
 
 
 
a
360.33
 
 
 
 
 
 
 
 
 
b
460.33
 
 
 
 
 
 
 
 
 
c
560.33
 
 
 
 
 
 
 
 
 
d
660.33
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
5
The estimated regression equation predicts that the expected wage rate for a person with 16 years of education is ______.
 
 
 
a
$29.45
 
 
 
 
 
 
 
 
 
b
$27.45
 
 
 
 
 
 
 
 
 
c
$25.45
 
 
 
 
 
 
 
 
 
d
$23.45
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
6
In the sample, the observed wage data deviate from the predicted wage, on average, by $ ________.
 
a
12.35
 
 
 
 
 
 
 
 
 
b
13.35
 
 
 
 
 
 
 
 
 
c
14.35
 
 
 
 
 
 
 
 
 
d
15.35
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
7
What proportion of the variations in wage can be explained by education?
 
 
 
a
0.1862
 
 
 
 
 
 
 
 
 
b
0.2262
 
 
 
 
 
 
 
 
 
c
0.3462
 
 
 
 
 
 
 
 
 
d
0.4562
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
8
The standard error of the slope coefficient is ______.
 
 
 
 
 
a
3.1606
 
 
 
 
 
 
 
 
 
b
2.1606
 
 
 
 
 
 
 
 
 
c
1.1606
 
 
 
 
 
 
 
 
 
d
0.9606
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
9
The 95% confidence interval for the population slope parameter is:
 
 
 
 
a
1.81
4.21
 
 
 
 
 
 
 
 
b
1.41
4.61
 
 
 
 
 
 
 
 
c
1.01
5.01
 
 
 
 
 
 
 
 
d
0.61
5.41
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
10
To test, at a 5% level of significance, the hypothesis H₀: β₁ = 0 versus H₁: β₁ ≠ 0, the t test statistic is 
|t| = ______.
 
 
 
a
2.593
Reject the null hypothesis.
 
 
 
 
 
 
b
2.935
Reject the null hypothesis.
 
 
 
 
 
 
c
3.277
Reject the null hypothesis.
 
 
 
 
 
 
d
3.619
Reject the null hypothesis.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Next TEN questions are based on the computer output below relating to the following problem
 
 
A regression model relating y, the annual sales (in thousands of dollars) at a branch office to x, number of salespersons at the office, provided the following regression summary output.
 
 
 
 
 
 
 
 
 
 
 
 
 
The exercise involves filling in the values for the numbered cells in yellow.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
SUMMARY OUTPUT
 
 
 
 
 
 
 
 
 
 
Regression Statistics
 
 
 
 
 
 
 
 
 
Multiple R
 
 
 
 
 
 
 
 
 
 
R Square
 
(5)
 
 
 
 
 
 
 
 
Adjusted R Square
 
 
 
 
 
 
 
 
 
Standard Error
(4)
 
 
 
 
 
 
 
 
Observations
(3)
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
ANOVA
 
 
 
 
 
 
 
 
 
 
 
df
SS
MS
F
Significance F
 
 
 
 
 
Regression
1
(2)
 
61.666
1.38E-05
 
 
 
 
 
Residual
28
(1)
82.1
 
 
 
 
 
 
 
Total
29
9127.4
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Coefficients
Std Error
t Stat
P-value
Lower 95%
Upper 95%
 
 
 
 
Intercept
80.246
11.333
7.081
1.06E-07
57.031
103.461
 
 
 
 
PERSONS
50.386
(6)
(7)
5.99E-10
(8)
(9)
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
11
How many branch offices were involved in the study?
 
 
 
 
 
a
29
 
 
 
 
 
 
 
 
 
b
30
 
 
 
 
 
 
 
 
 
c
31
 
 
 
 
 
 
 
 
 
d
32
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
12
The predicted annual sales at an office with 12 salespersons is $______ thousand.
 
 
 
a
$714.88
 
 
 
 
 
 
 
 
 
b
$704.88
 
 
 
 
 
 
 
 
 
c
$694.88
 
 
 
 
 
 
 
 
 
d
$684.88
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
13
The value for SSE in (1) is:
 
 
 
 
 
 
 
a
2198.8
 
 
 
 
 
 
 
 
 
b
2298.8
 
 
 
 
 
 
 
 
 
c
2398.8
 
 
 
 
 
 
 
 
 
d
2498.8
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
14
The variance of the prediction error is ______
 
 
 
 
 
 
a
2298.8
 
 
 
 
 
 
 
 
 
b
47.95
 
 
 
 
 
 
 
 
 
c
82.1
 
 
 
 
 
 
 
 
 
d
9.06
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
15
The value for SSR in (2) is:
 
 
 
 
 
 
 
a
6828.6
 
 
 
 
 
 
 
 
 
b
6928.6
 
 
 
 
 
 
 
 
 
c
7028.6
 
 
 
 
 
 
 
 
 
d
7128.6
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
16
The value for the standard error of estimate se(e) in (4) is:
 
 
 
 
a
9.303
 
 
 
 
 
 
 
 
 
b
9.061
 
 
 
 
 
 
 
 
 
c
8.819
 
 
 
 
 
 
 
 
 
d
8.577
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
17
The value for R² in (5) is:
 
 
 
 
 
 
 
a
0.8513
 
 
 
 
 
 
 
 
 
b
0.8169
 
 
 
 
 
 
 
 
 
c
0.7825
 
 
 
 
 
 
 
 
 
d
0.7481
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
18
Given ∑(x − x̅)² = 2.732, the value of the standard error of the slope coefficient in (6) is:
 
 
a
6.013
 
 
 
 
 
 
 
 
 
b
5.482
 
 
 
 
 
 
 
 
 
c
4.951
 
 
 
 
 
 
 
 
 
d
4.420
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
19
The value of the t stat |t| in (7) is:
 
 
 
 
 
 
 
a
10.876
 
 
 
 
 
 
 
 
 
b
9.191
 
 
 
 
 
 
 
 
 
c
7.506
 
 
 
 
 
 
 
 
 
d
5.821
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
20
The lower and upper end of a 95% confidence interval for the population slope parameter β₁ in (8) and (9), respectively, are:
 
 
 
a
34.432
66.340
 
 
 
 
 
 
 
 
b
36.001
64.771
 
 
 
 
 
 
 
 
c
39.159
61.613
 
 
 
 
 
 
 
 
d
42.150
58.622
 
 
 
 
 
 
 
 
 
 
 
 
 

 
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