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:1 Country 2 Bangladesh 3 Tanzania 4 Sierra Leone 5 Sudan 6 Kenya 7 Indonesia 8 Panama 9 Chile 10 Venezuela 11 Turkey 12 Malaysia 13 Nepal 14 Malawi 15 Argentina 16 17 Mean 18 St Dev 19 Correlation Coeficient GNP per cap Birth Rate 5200 Chart Title y=0.0011x + 30.944 R= 0.5451 18 40 2700 36 35 1770 33 30 3990 32 25 4430 29 20 15 11970 18 10 15730 19 14890 12 16054 18 18000 2000 4000 6000 8000 10000 12000 14000 16000 9120 16 GNP per Capita 11410 15 1070 19 410 34 SUMMARY OUTPUT 9910 17 Regression Statistics 7761 22.57142857 Multiple R 0.775729 5634.950153 R Square 8.234208997 0.601755 Adjusted F 0.565551 Standard E 5.576425 Observatic -0.738279458 -0.738279458 20 21 22 23 13 ANOVA izificance F 24 25 26 27 28 29 30 31 of Regression Residual Total 516.8614 516.8614 16.6212 0.00183 11 342.0617 12 858.9231 31.09652 Caefficienttandand En 31.90516 5200 -0.001129 0.000277 Stat Fvalue Lower 9oper 95X.ower 950pner 950% 1.32E-07 25.98048 37.82984 25.98048 37.82984 0.00183 -0.001738 -0.000519 -0.001738 -0.000519 Intercept 2.69183 11.85259 -4.07691 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 RESIDUAL OUTPUT CbservativFredicted Residals 1 28.85771 7.142293 2 29.90739 3.092615 27.4017 4.598297 4 26.90508 18.39479 -0.394789 2.094919 6 14.15093 4.84907 7 15.09903 -3.099026 13.78524 4.214764 9 21.61154 -5.611544 10 19.02685 -4.026853 11 30.69747 -11.69747 12 31.4424 2.557602 13 20.71988 -3.719882 Birth Rate
Transcribed Image Text:Section A (i) (ii) Comment on the scatterplot: form, 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 1. Data on GNP per capita and Birth Rate (births per thousand inhabitants) for a sample of 14 countries for 2019 is displayed below: (iii) (iv) GNP Birth Country per cap Rate (v) Bangladesh 5200 18 Tanzania 2700 36 (vi) stat. The distribution to test for the coefficient is T distribution n-2 Sierra degrees of freedom. Show all workings. Leone 1770 33 (vii) Look up the T table and verify the P value. What line along the T table should you use to check the p value for the t stat? (viii) Write out how to calculate the residual for Nepal (you can check your Sudan 3990 32 Kenya 4430 29 manual result matches the excel output). Show all workings. Indonesia 11970 18 (ix) Comment on the residual. (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 Panama 15730 19 Chile 14890 12 Venezuela 16054 18 (xi) Turkey Malaysia Nepal 9120 16 would you expect its birth rate to be? Show all workings. (xii) Using the Bsquared from the regression output calculate the correlation coefficient manually. Show all workings. 11410 15 1070 19 (xii) This dataset is not necessarily random. Is GNP per capita a good way to Malawi 410 34 Argentina determine a country's birth rate? Comment with reference to two countries from this dataset. 9910 17 Copy the data into excel. (Or use the excel file containing the data uploaded to Moodle) (i) a. Generate summary statistics for correlation coefficient and mean and standard deviation for each variable. (ii) (ii) Generate a scatterplot of birth rate vs gng per capita. Generate the line of best fit where gng is the explanatory variable for birth rate, the response variable. (iv) Display equation for line of best fit on the graph. (v) (vi) Display R squared on the graph. Generate regression summary.

Question

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.

1 Country
2 Bangladesh
3 Tanzania
4 Sierra Leone
5 Sudan
6 Kenya
7 Indonesia
8 Panama
9 Chile
10 Venezuela
11 Turkey
12 Malaysia
13 Nepal
14 Malawi
15 Argentina
16
17 Mean
18 St Dev
19 Correlation Coeficient
GNP per cap Birth Rate
5200
Chart Title
y=0.0011x + 30.944
R= 0.5451
18
40
2700
36
35
1770
33
30
3990
32
25
4430
29
20
15
11970
18
10
15730
19
14890
12
16054
18
18000
2000
4000
6000
8000
10000
12000
14000
16000
9120
16
GNP per Capita
11410
15
1070
19
410
34
SUMMARY OUTPUT
9910
17
Regression Statistics
7761
22.57142857
Multiple R 0.775729
5634.950153
R Square
8.234208997
0.601755
Adjusted F 0.565551
Standard E 5.576425
Observatic
-0.738279458 -0.738279458
20
21
22
23
13
ANOVA
izificance F
24
25
26
27
28
29
30
31
of
Regression
Residual
Total
516.8614
516.8614
16.6212
0.00183
11
342.0617
12
858.9231
31.09652
Caefficienttandand En
31.90516
5200 -0.001129 0.000277
Stat
Fvalue Lower 9oper 95X.ower 950pner 950%
1.32E-07 25.98048 37.82984 25.98048 37.82984
0.00183 -0.001738 -0.000519 -0.001738 -0.000519
Intercept
2.69183
11.85259
-4.07691
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
RESIDUAL OUTPUT
CbservativFredicted Residals
1 28.85771 7.142293
2 29.90739
3.092615
27.4017 4.598297
4 26.90508
18.39479 -0.394789
2.094919
6
14.15093
4.84907
7
15.09903 -3.099026
13.78524
4.214764
9
21.61154
-5.611544
10
19.02685 -4.026853
11 30.69747 -11.69747
12
31.4424 2.557602
13
20.71988 -3.719882
Birth Rate

Section A
(i)
(ii)
Comment on the scatterplot: form, 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
1. Data on GNP per capita and Birth Rate (births per thousand inhabitants) for a sample
of 14 countries for 2019 is displayed below:
(iii)
(iv)
GNP
Birth
Country
per cap
Rate
(v)
Bangladesh
5200
18
Tanzania
2700
36
(vi)
stat. The distribution to test for the coefficient is T distribution n-2
Sierra
degrees of freedom. Show all workings.
Leone
1770
33
(vii) Look up the T table and verify the P value. What line along the T table
should you use to check the p value for the t stat?
(viii) Write out how to calculate the residual for Nepal (you can check your
Sudan
3990
32
Kenya
4430
29
manual result matches the excel output). Show all workings.
Indonesia
11970
18
(ix)
Comment on the residual.
(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
Panama
15730
19
Chile
14890
12
Venezuela
16054
18
(xi)
Turkey
Malaysia
Nepal
9120
16
would you expect its birth rate to be? Show all workings.
(xii) Using the Bsquared from the regression output calculate the correlation
coefficient manually. Show all workings.
11410
15
1070
19
(xii) This dataset is not necessarily random. Is GNP per capita a good way to
Malawi
410
34
Argentina
determine a country's birth rate? Comment with reference to two
countries from this dataset.
9910
17
Copy the data into excel. (Or use the excel file containing the data uploaded to
Moodle)
(i)
a.
Generate summary statistics for correlation coefficient and mean and
standard deviation for each variable.
(ii)
(ii)
Generate a scatterplot of birth rate vs gng per capita.
Generate the line of best fit where gng is the explanatory variable for
birth rate, the response variable.
(iv) Display equation for line of best fit on the graph.
(v)
(vi)
Display R squared on the graph.
Generate regression summary.

Accepted Answer

Regression equation is given by,
Y= a+bX 
Where a is intercept and b is slope.
Here a= 31.90516
b=…