further maths core SAC

[doboman]

Question 4. Write a report on the results of the regression analysis.
My answer was:
from the scatterplot we can see that there is a moderate positive, linear relationship between the co2 levels and GNI of Sub-Saharan Africa, r=0.5964. There are no obvious outliers. The equation of the least squares regression line is:

GNI= -2144.11315 + (2866.972477 x co2 level)

The slope of the regression line predicts that, on average, GNI increases by 2866.972477 per ton of co2.

The coefficient of determination indicates that 35.6% of the variation in GNI is explained by the variation in co2 level.

The residual plot shows no clear pattern, indicating that the data has a linear relationship.


(this question is worth 5 marks, how many have i earnt, and what can i improve).

Everything else other than the parts i bolded is fine. You can't just write "no obvious outliers", as that is wrong. You have to actually decipher the data, and give a definite answer. That is done be the formula 1.5 x ..... So after you find out whether there are any outliers,you must write it definitively and provide reasoning (mathematically).
For the second one, you must be consistant with your description of the independant variable. In the formula, you wrote "co2 level" and in the written explination you wrote "per ton of co2". Just be consistant and you should be fine.

Hope i didn't miss anything. Good luck

[methodsboy]

sorry, didnt have the time at that particular moment.


well i had to randomly select data off a sheet, the data showed different regions, and then displayed that regions Co2 emissions and the regions GNI (gross national income). After randomly selecting a region, i was asked to select a starting year between 1970 and 2000 and then a continuous period of 12 years.

The data i randomly selected is as follows:

Sub-Saharan Africa                                        
year              Co2 emissions            GNI

1972:              0.88                       230
1973:              0.91                       270
1974:              0.94                       360
1975:              0.89                       410
1976:              0.91                       430
1977:              0.88                       450
1978:              0.86                       470
1979:              0.94                       560
1980:              0.93                       660
1981:              0.96                       700
1982:              0.94                       650
1983:              0.94                       560


Most of the questions relate to comparing or displaying my regions data against the data for the world.
the worlds data is as follows:

year              Co2 emissions            GNI

1972:              4.00                       960
1973:              4.12                       1160
1974:              4.03                       1360
1975:              3.97                       1520
1976:              4.13                       1590
1977:              4.16                       1690
1978:              4.25                       1900
1979:              4.29                       2240
1980:              4.20                       2570
1981:              4.03                       2660
1982:              3.94                       2520
1983:              3.91                       2390

___________________________________________________________________________________________________________________

Question 1. construct a scatterplot to investigate the nature of the relationship between Co2 emissions (as the independant variable) and the GNI for your selected region.

Question 2. assuming the relationship is linear, use the scatterplot data to perform a full regression analysis. ie. calculate the equation of the least squares regression line, calculate the correlation coefficient and the coefficient of determination, and graph a residual plot. (provide a sketch of the residual plot).

Question 3. Use the equation to interpolate and extrapolate (one value of each) within the range of the original data supplied. Comment on the reliability of each of these predictions.

Question 4. Write a report on the results of the regression analysis.

Question 5. Based on your regression analysis, discuss the suitability of using a linear model to represent the data. If the data was non-linear, suggest appropriate transformations that may linearise the relationship between the co2 emissions and GNI. Explain how these transformations would linearise the data.

Question 6. construct a time series plot of co2 emissions for your selected region and time for the world on one set of axes.

Question 7. comment on any trends in the two time series plots.

Question 8. Assuming the data is linear, find the equation of the least squares regression trend line for each set of data. Use the trend lines to forecast the co2 emissions for your selected region and for the world in 2010.






PLEASE HELP

whoa; nice post =]

[ReVeL]

Question 4. Write a report on the results of the regression analysis.
My answer was:
from the scatterplot we can see that there is a moderate positive, linear relationship between the co2 levels and GNI of Sub-Saharan Africa, r=0.5964. There are no obvious outliers. The equation of the least squares regression line is:

GNI= -2144.11315 + (2866.972477 x co2 level)

The slope of the regression line predicts that, on average, GNI increases by 2866.972477 per ton of co2.

The coefficient of determination indicates that 35.6% of the variation in GNI is explained by the variation in co2 level.

The residual plot shows no clear pattern, indicating that the data has a linear relationship.


(this question is worth 5 marks, how many have i earnt, and what can i improve).

In the opening line you say "from the scatterplot". I would probably say "after calculating the correlation of and looking at the scatterplot, it can be said there is a moderate positive linear relationship..."

I would perhaps also add that because 35.6% of the variation in GNI can be explained by the variation in co2 level, 64.4% can be explained by other factors. Small add-on, but worth saying.

Umm yeah as methodsboy said, you would want to prove conclusively that there are or aren't any outliers rather than just estimating. Other than that it's fine I think.