I have completed the requested questions on section 1 a on excel however I am having a bit of trouble analysing this data and awnsering 1 b and it's sub questions. please help me solve these 3 sub questions (iv) Write out the regression equation, (you can check that your manual calculations match the regression output in excel). (v) Form a hypothesis about the effect of GNP per capita on birth rate and state the hypothesis. Test the hypothesis at a significance level of 0.05. (vi)Write out the formula to calculate the T stat, and manually calculate the T stat. The distribution to test for the coefficient is T distribution n-2 degrees of freedom. Show all workings manually, using the summary statistics you generated in excel (correlation coefficient, standard deviation of y and standard deviation of x). Show all workings. The comment must be done on the work I have already done on excel. Please help,thank you.
I have completed the requested questions on section 1 a on excel however I am having a bit of trouble analysing this data and awnsering 1 b and it's sub questions. please help me solve these 3 sub questions (iv) Write out the regression equation, (you can check that your manual calculations match the regression output in excel). (v) Form a hypothesis about the effect of GNP per capita on birth rate and state the hypothesis. Test the hypothesis at a significance level of 0.05. (vi)Write out the formula to calculate the T stat, and manually calculate the T stat. The distribution to test for the coefficient is T distribution n-2 degrees of freedom. Show all workings manually, using the summary statistics you generated in excel (correlation coefficient, standard deviation of y and standard deviation of x). Show all workings. The comment must be done on the work I have already done on excel. Please help,thank you.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Good Afternoon
I have completed the requested questions on section 1 a on excel however I am having a bit of trouble analysing this data and awnsering 1 b and it's sub questions.
please help me solve these 3 sub questions
- (iv) Write out the regression equation, (you can check that your manual calculations match the regression output in excel).
- (v) Form a hypothesis about the effect of GNP per capita on birth rate and state the hypothesis. Test the hypothesis at a significance level of 0.05.
- (vi)Write out the formula to calculate the T stat, and manually calculate the T stat. The distribution to test for the coefficient is T distribution n-2 degrees of freedom. Show all workings manually, using the summary statistics you generated in excel (
correlation coefficient , standard deviation of y and standard deviation of x). Show all workings.
The comment must be done on the work I have already done on excel.
Please help,thank you.
Transcribed Image Text:|Country
Bangladesh
GNP per cap Birth Rate
5200
y= 0.0011x + 30.944
R=0.5451
18
40
Tanzania
2700
36
35
Sierra Leone
1770
3990
33
30
Sudan
32
25
Kenya
4430
29
20
15
Indonesia
11970
18
10
Panama
15730
19
Chile
14890
12
Venezuela
Turkey
Malaysia
Nepal
16054
18
BO00 10000 12000
2000
4000
6000
14000
16000
18000
9120
16
GNP per Capita
11410
15
1070
19
Malawi
410
34
|Argentina
9910
17
SUMMARY OUTPUT
Mean
St Dev
Correlation Coeficient
7761
22.57142857
Regression Statistics
5634.950153 8.234208997
Multiple R 0.738279
-0.738279458 -0.738279458
RSquare
Adjusted F 0.507145
Standard E 5.780716
Observatic
0.545057
14
ANOVA
27ficace F
14.37691 0.002568
of
Regressior
1 480.4284 480.4284
12
401.0001
13
881.4286
Residual
33.41668
Total
Coefficientandand En
Fvalue Lower %oper 95X.ower 950pner 950%
36.81612 25.07232 36.81612
X Variable -0.001079 0.000285 -3.791689 0.002568 -0.001699 -0.000459 -0.001699 -0.000459
Siat
Intercept
30.94422 2.695002
11.48208 7.89E-08 25.07232
SUMMARY OUTPUT
Regression Satisties
Multiple R 13.84197
R Square
Adjusted F 20.19379
Standard E
Observatic 26.54561
17.01788
23.3697
Transcribed Image Text:enezuela
anama
1 Country
2 Bangladesh
Tanzania
GNP per cap Birth Rate
5200
Chart Title
y0.001ix+30.544
18
3
2700
36
4 Sierra Leone
5 Sudan
6 Kenya
1770
33
3990
32
4430
29
- Indonesia
11970
15730
7
18
Comment on the scatterplot: orm, strength, direction, outliers.
Demonstrate how to calculate the slope of the regression line manually,
using the summary statistics you generated in excel (correlation
coefficient, standard deviation of y and standard deviation of x). Show all
workings.
Now calculate the intercept, manually. Show all workings.
Write out the regression equation, (you can check that your manual
calculations match the regression output in excel).
Form a hypothesis about the effect of GNP per capita on birth rate and
state the hypothesis. Test the hypothesis at a significance level of 0.05.
Write out the formula to calculate the T stat, and manually calculate the T
stat. The distribution to test for the coefficient is I distribution n-2
tion A
()
(i)
8 Panama
9 Chile
10 Venezuela
11 Turkey
12 Malaysia
13 Nepal
Malawi
15 Argentina
16
17 Mean
10
19
1. Data on GNP per capita and Birth Rate (births per thousand inhabitants) for a sample
of 14 countries for 2019 is displayed below:
14890
16054
12
18
2000
4000
6000
8000
10000
12000
14000
16000
18000
GNP per Capita
(i)
(iv)
9120
16
GNP
Birth
11410
15
ountry
angladesh
per cap Rate
(v)
1070
19
5200
18
410
34
SUMMARY OUTPUT
14
anzania
2700
36
(vi)
9910
17
jerra
Recression Siatistics
Multiple R 0.775729
degrees of freedom. Show all workings.
eone
1770
33
(vii) Look up the T table and verify the P value. What line along the T table
7761 22.57142857
udan
should you use to check the p value for the t stat?
18 St Dev
19 Correlation Coeficient
3990
32
(viii) Write out how to calculate the residual for Nepal (you can check your
5634.950153 8.234208997
RSquare
0.601755
enva
4430
29
manual result matches the excel output). Show all workings.
-0.738279458 -0.738279458
Adjusted F 0.565551
Standard E 5,576425
Observatic
idonesia
(ix)
Comment on the residual.
20
21
11970
18
(x)
This is updated data for the 14 countries studied in the in-class mock
exam. Compare the regression equation from the 1980s data used in the
exam with this data from 2019 and comment on one similarity and one
difference between the two time periods.
If the GNP per capita of Malawi were to increase by US$ 1000, what
13
15730
19
22
23
hile
14890
12
ANOVA
16056
18
vificarce F
0.00183
24
25
26
27
of
MS
516.8614
F
(xi)
urkey
lalaysia
еpal
lalawi
Regression
Residual
Total
9120
16
1
516.8614
16.6212
would you expect its birth rate to be? Show all workings.
11
342.0617 3109652
11410
15
Using the Bsquared from the regression output calculate the correlation
coefficient manually. Show all workings.
(xii)
12
858.9231
1070
19
28
(xiii) This dataset is not necessarily random. Is GNP per capita a good way to
determine a country's birth rate? Comment with reference to two
29
30
31
Coefficientantard En Sa
3190516
5200 -0.001129 0.000277
Pvalue Lower S5%Loper 95%.ower 25 0pper 25 0%
11.85259 1.32E-07 25.98048 37.82984 25.98048 37.82984
0.00183 -0.001738 -0.000519 -0.001738 -0.000519
410
34
rgentina
9910
17
Intercept
2.69183
countries from this dataset.
-4.07691
32
33
34
a. Copy the data into excel. (Or use the excel file containing the data uploaded to
Moodle)
35
RESIDUAL OUTPUT
36
CbservatiovFredcted R Residuals
1 28.85771
(1)
Generate summary statistics for correlation coefficient and mean and
standard deviation for each variable.
Generate a scatterplot of birth rate vs gnp per capita.
Generate the line of best fit where gop is the explanatory variable for
birth rate, the response variable.
Display equation for line of best fit on the graph.
Display R squared on the graph.
Generate regression summary.
37
38
39
40
41
7.142293
(ii)
(i)
2 29.90739 3.092615
3
27.4017 4.598297
26.90508
18.39479 -0.394789
4
2.094919
(iv)
(V)
(vi)
42
5
43
6
14.15093
4.84907
44
45
46
15.09903 -3.099026
8 13.78524 4.214764
21.61154 -5.611544
19.02685 -4.026853
7
47
10
48
49
50
30.69747 -1169747
12
11
31.4424 2.557602
13
20.71988 -3.719882
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