Soal dan Jawaban Statistika 2 LInd March
PRESENTASI
SOAL dan
JAWABAN
STATISTIKA-WEEK 4
Question 1
Mike Wilde is president of the teachers’ union for Otsego School
District. In preparing for upcoming negotiations, he would like to
investigate the salary structure of classroom teachers in the district.
He believes there are three factors that affect a teacher’s salary: years
of experience, a rating of teaching effectiveness given by the
principal, and whether the teacher has a master’s degree. A random
sample of 20 teachers resulted in the following data.
TABLE DATA
*1 = yes, 0 = no.
Develop a correlation matrix. Which independent variable
has the strongest correlation with the dependent variable?
Does it appear there will be any problems with
multicollinearity?
Salary
Salary
Years of
Experience, X1
Principal’s
Rating, X2
Master's Degree
Years of
Experience, X1
Principal’s
Rating, X2
Master's Degree
1
0,577299
1
0,442869
-0,32744
1
-0,37181
-0,80861
0,373321
Strongest Correlation:
=> Salary with Years of
Experience
1
Problem with multicollineary:
Yes. Because there is -0.80861
(more than -0.7)
Determine the regression equation. What salary
would you estimate for a teacher with five years
experience, a rating by the principal of 60, and no
masters degree?-continued
Determine the regression equation. What salary
would you estimate for a teacher with five years
experience, a rating by the principal of 60, and no
masters degree?-last-
▸ Regression Equation:
The estimated salary for a teacher with five years
experience, a rating by the principal of 60, and no
master degree is 36,6658 (in thousand US$)
Conduct a global test hypothesis to determine
whether any of the regression coefficients differ
from zero. Use the .05 significance level.
Bring the attention
of your audience
over a key concept
using icons or
illustrations
Conduct a test of hypothesis for the individual
regression coefficients. Would you consider
deleting any of the independent variables? Use
the .05 significance level.
▸
▸
▸
Using the regression table, the t ratio of years experience is 1,5131 and the p
values of Years experience is 0.2694. Because the p value is more than 0.05,
we conclude that the years expereince regression coefficient could equal 0.
Thus, years of experience should not be included in the equation to predict a
teacher’s salary.
The t ratio of principal’s rating is 1,9658 and the p value is 0,1882. The p
value is more than 0.05 the principal rating could equal 0. So, principal’s
rating should not be included in the equation topredict teachers salary.
The t ratio of master degree is 0,0952 and the p value is 0,9328. The p value
is more than 0.05 the principal rating could equal 0. So, principal’s rating
should not be included in the equation topredict teachers salary.
If your conclusion in part (d) was to delete one
or more independent variables, run
the analysis again without those variables.
▸ Without Master degree
E. SUMMARY OUTPUT
Regression Statistics
Multiple R
0,883472994
R Square
0,78052453
Adjusted R
Square
0,634207551
Standard Error
2,939992117
Observations
6
ANOVA
df
Regression
Residual
Total
Intercept
X Variable 1
X Variable 2
2
3
5
Significance
SS
MS
F
F
92,21767238 46,10883619 5,334477 0,102820327
25,93066095 8,643553651
118,1483333
Coefficients Standard Error
t Stat
P-value Lower 95% Upper 95%
15,00446535
6,017721046 2,493380007 0,08822 -4,146608764 34,1555395
1,449013691
0,512687599 2,826309227 0,066392 -0,182587063 3,08061445
0,198984871
0,080477956 2,472538834 0,089862 -0,057131902 0,45510165
Lower
95,0%
Upper 95,0%
-4,14660876 34,15553945
-0,18258706 3,080614445
-0,0571319 0,455101645
F.
90
80
70
60
50
40
30
20
10
0
Gaji (ribu $)
penilaian kepala sekolah,
pengalaman mengajar (tahun),
45
G.
40
35
Residu
30
25
20
15
10
5
0
28
30
32
34
36
Ŷ
38
40
42
44
Question 2 - 44
▸ A sample of 12 homes sold last week in St. Paul, Minnesota,
is selected. Can we conclude that, as the size of the home
(reported below in thousands of square feet) increases, the
selling price (reported in $ thousands) also increases?
a. Compute the correlation
coefficient.
Home Size
Selling Price
Mean
1,15
Mean
96,66666667
Standard Error
0,054355731
Standard Error
4,536607552
Median
1,15
Median
102,5
Mode
1,1
Mode
105
Standard Deviation
0,188293774
Standard Deviation
15,71526955
Sample Variance
0,035454545
Sample Variance
246,969697
Kurtosis
-0,488888889
Kurtosis
-0,943584629
Skewness
-0,39218585
Skewness
-0,453624695
Range
0,6
Range
50
Minimum
0,8
Minimum
70
Maximum
1,4
Maximum
120
Sum
13,8
Sum
1160
Count
12
Count
12
a. Compute the correlation
coefficient.
Home Size
Selling Price
X - X
Y - Y
(X - X)(y - y)
1,4
100
0,25
3,333333333
0,833333333
1,3
110
0,15
13,33333333
2
1,2
105
0,05
8,333333333
0,416666667
1,1
120
-0,05
23,33333333
-1,166666667
1,4
80
0,25
-16,66666667
-4,166666667
1
105
-0,15
8,333333333
-1,25
1,3
110
0,15
13,33333333
2
0,8
85
-0,35
-11,66666667
4,083333333
1,2
105
0,05
8,333333333
0,416666667
0,9
75
-0,25
-21,66666667
5,416666667
1,1
70
-0,05
-26,66666667
1,333333333
1,1
95
-0,05
-1,666666667
0,083333333
10
a. Compute the correlation
coefficient.
Correlation Coefficient :
X-X
b. Determine the coefficient of
determination.
▸ The relationship is positive or direct, because the sign of
the correlation coefficient is positive. As the size of the
home (reported in thousands of square feet) increases, the
selling price (reported in $ thousands) also increases
increases.
▸ The relationship between the two variables is weak
positive correlation. If the values of the correlation
coefficient is close to one, its indicate stronger
relationships.
▸ In this case, r = 0.375. It is closer to zero, and we would
observe that the relationship is not very strong.
c. Can we conclude that there is a positive
association between the size of the home and the
selling price? Use the .05 significance level.
H0 is rejected. There is a positive association
between home size and selling price.
SOAL dan
JAWABAN
STATISTIKA-WEEK 4
Question 1
Mike Wilde is president of the teachers’ union for Otsego School
District. In preparing for upcoming negotiations, he would like to
investigate the salary structure of classroom teachers in the district.
He believes there are three factors that affect a teacher’s salary: years
of experience, a rating of teaching effectiveness given by the
principal, and whether the teacher has a master’s degree. A random
sample of 20 teachers resulted in the following data.
TABLE DATA
*1 = yes, 0 = no.
Develop a correlation matrix. Which independent variable
has the strongest correlation with the dependent variable?
Does it appear there will be any problems with
multicollinearity?
Salary
Salary
Years of
Experience, X1
Principal’s
Rating, X2
Master's Degree
Years of
Experience, X1
Principal’s
Rating, X2
Master's Degree
1
0,577299
1
0,442869
-0,32744
1
-0,37181
-0,80861
0,373321
Strongest Correlation:
=> Salary with Years of
Experience
1
Problem with multicollineary:
Yes. Because there is -0.80861
(more than -0.7)
Determine the regression equation. What salary
would you estimate for a teacher with five years
experience, a rating by the principal of 60, and no
masters degree?-continued
Determine the regression equation. What salary
would you estimate for a teacher with five years
experience, a rating by the principal of 60, and no
masters degree?-last-
▸ Regression Equation:
The estimated salary for a teacher with five years
experience, a rating by the principal of 60, and no
master degree is 36,6658 (in thousand US$)
Conduct a global test hypothesis to determine
whether any of the regression coefficients differ
from zero. Use the .05 significance level.
Bring the attention
of your audience
over a key concept
using icons or
illustrations
Conduct a test of hypothesis for the individual
regression coefficients. Would you consider
deleting any of the independent variables? Use
the .05 significance level.
▸
▸
▸
Using the regression table, the t ratio of years experience is 1,5131 and the p
values of Years experience is 0.2694. Because the p value is more than 0.05,
we conclude that the years expereince regression coefficient could equal 0.
Thus, years of experience should not be included in the equation to predict a
teacher’s salary.
The t ratio of principal’s rating is 1,9658 and the p value is 0,1882. The p
value is more than 0.05 the principal rating could equal 0. So, principal’s
rating should not be included in the equation topredict teachers salary.
The t ratio of master degree is 0,0952 and the p value is 0,9328. The p value
is more than 0.05 the principal rating could equal 0. So, principal’s rating
should not be included in the equation topredict teachers salary.
If your conclusion in part (d) was to delete one
or more independent variables, run
the analysis again without those variables.
▸ Without Master degree
E. SUMMARY OUTPUT
Regression Statistics
Multiple R
0,883472994
R Square
0,78052453
Adjusted R
Square
0,634207551
Standard Error
2,939992117
Observations
6
ANOVA
df
Regression
Residual
Total
Intercept
X Variable 1
X Variable 2
2
3
5
Significance
SS
MS
F
F
92,21767238 46,10883619 5,334477 0,102820327
25,93066095 8,643553651
118,1483333
Coefficients Standard Error
t Stat
P-value Lower 95% Upper 95%
15,00446535
6,017721046 2,493380007 0,08822 -4,146608764 34,1555395
1,449013691
0,512687599 2,826309227 0,066392 -0,182587063 3,08061445
0,198984871
0,080477956 2,472538834 0,089862 -0,057131902 0,45510165
Lower
95,0%
Upper 95,0%
-4,14660876 34,15553945
-0,18258706 3,080614445
-0,0571319 0,455101645
F.
90
80
70
60
50
40
30
20
10
0
Gaji (ribu $)
penilaian kepala sekolah,
pengalaman mengajar (tahun),
45
G.
40
35
Residu
30
25
20
15
10
5
0
28
30
32
34
36
Ŷ
38
40
42
44
Question 2 - 44
▸ A sample of 12 homes sold last week in St. Paul, Minnesota,
is selected. Can we conclude that, as the size of the home
(reported below in thousands of square feet) increases, the
selling price (reported in $ thousands) also increases?
a. Compute the correlation
coefficient.
Home Size
Selling Price
Mean
1,15
Mean
96,66666667
Standard Error
0,054355731
Standard Error
4,536607552
Median
1,15
Median
102,5
Mode
1,1
Mode
105
Standard Deviation
0,188293774
Standard Deviation
15,71526955
Sample Variance
0,035454545
Sample Variance
246,969697
Kurtosis
-0,488888889
Kurtosis
-0,943584629
Skewness
-0,39218585
Skewness
-0,453624695
Range
0,6
Range
50
Minimum
0,8
Minimum
70
Maximum
1,4
Maximum
120
Sum
13,8
Sum
1160
Count
12
Count
12
a. Compute the correlation
coefficient.
Home Size
Selling Price
X - X
Y - Y
(X - X)(y - y)
1,4
100
0,25
3,333333333
0,833333333
1,3
110
0,15
13,33333333
2
1,2
105
0,05
8,333333333
0,416666667
1,1
120
-0,05
23,33333333
-1,166666667
1,4
80
0,25
-16,66666667
-4,166666667
1
105
-0,15
8,333333333
-1,25
1,3
110
0,15
13,33333333
2
0,8
85
-0,35
-11,66666667
4,083333333
1,2
105
0,05
8,333333333
0,416666667
0,9
75
-0,25
-21,66666667
5,416666667
1,1
70
-0,05
-26,66666667
1,333333333
1,1
95
-0,05
-1,666666667
0,083333333
10
a. Compute the correlation
coefficient.
Correlation Coefficient :
X-X
b. Determine the coefficient of
determination.
▸ The relationship is positive or direct, because the sign of
the correlation coefficient is positive. As the size of the
home (reported in thousands of square feet) increases, the
selling price (reported in $ thousands) also increases
increases.
▸ The relationship between the two variables is weak
positive correlation. If the values of the correlation
coefficient is close to one, its indicate stronger
relationships.
▸ In this case, r = 0.375. It is closer to zero, and we would
observe that the relationship is not very strong.
c. Can we conclude that there is a positive
association between the size of the home and the
selling price? Use the .05 significance level.
H0 is rejected. There is a positive association
between home size and selling price.