• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month
Page
  1. 1
    1
  2. 2
    2
  3. 3
    3
  4. 4
    4
  5. 5
    5
  6. 6
    6
  7. 7
    7
  8. 8
    8
  9. 9
    9
  • Level: GCSE
  • Subject: Maths
  • Word count: 5329

Correlation and regression

Extracts from this document...

Introduction

Ibrar KhanAS Use of mathematics coursework

Correlation and regression

Background information

In statistics, correlation often indicates the strength and direction of a linear relationship between two random variables. If there is no correlation between the two sets of data, the points will be widely scattered and will require a circular shape to enclose them. If the two sets of data have weak positive correlation, the points can be modelled in a broad eclipse sloping upwards from bottom left to top right. Furthermore if the two sets of data have a strong positive correlation, the points lie within a narrow eclipse sloping upwards.

If the two sets of data have weak negative correlation, where one quantity generally increases as the other one decreases, the points can be modelled in a broad eclipse sloping downards from top left to bottom right. If the two sets of data have a strong positive correlation, the points lie within a narrow eclipse sloping downwards.

Finally ‘perfect’ positive correlation (a correlation co-efficient of +1) implies that as one variable moves, either up or down, the other variable will move in lockstep, in the same direction. Alternatively, ‘perfect’ negative correlation means that if one variable moves in either direction the variable that is perfectly negatively correlated will move by an equal amount in the opposite direction, also when all the data points on a scatter diagram accumulate on a straight line we say that they are perfectly positively or negatively correlated.

A correlation coefficient is a number between -1 and +1, which measures the degree to which two variables are linearly related. If there is perfect linear relationship with positive slope between the two variables, we have a correlation coefficient of +1; if there is positive correlation, whenever one variable has a high (low) value, so does the other.

...read more.

Middle

th value. The 18 th value in my case is ‘29’ marks, so therefore, the median mark for the female population on the non-calculator written paper (Paper 1) is 29 marks.

After finding the median marks for the non-calculator written paper (Paper 1) of the male and female populations, I can quite honestly articulate that so far my prediction of ‘the male population will have higher marks on the non-calculator written paper (Paper 1) and the calculator written paper (Paper 2) than the female population’ is true and accurate because the median marks for the non-calculator written paper (Paper 1) of the male population was ‘35’ marks, whereas the female population was only ‘29’ marks.

Next, I am going to find the median marks on the calculator written paper (Paper 2) for both the male and female populations by doing a similar process as above.

Starting with the calculator written paper (Paper 2) for the male population.

0.5 (29 + 1) = 15 th value

Then you start with the highest mark, which for the male population on the calculator written paper (Paper 2) was ‘46’ marks and count along, next being ‘45’ and then ‘45’ and so on until you reach the 15 th value. The 15 th value in my case is ‘30’ marks, so therefore, the median mark for the male population on the calculator written paper (Paper 2) is 30 marks.

Next, the calculator written paper (Paper 2) for the female population.

0.5 (35 + 1) = 18 th value

Then you start with the highest mark, which for the female population on the calculator written paper (Paper 2) was ‘51’ marks and count along, next being ‘47’ and then ‘42’ and so on until you reach the 18 th value. The 18 th value in my case is ‘26’ marks, so therefore, the median mark for the female population on the calculator written paper (Paper 2) is 26 marks.

After finding the median marks for the non-calculator written paper (Paper 1) and the calculator written paper (Paper 2)

...read more.

Conclusion

 1, which would indicate strong positive correlations.

Hypothesis

For my new hypothesis I am going to compare the correlation coefficients of the male and female population in terms of the mental test and the calculator written paper (Paper 2) results. On this occasion I predict that ‘the correlation coefficient for the female population will be larger than the correlation coefficient for the male population. Furthermore I again predict the values of the correlation coefficients for both the male and female population to be between 0.5 < r  1, which would indicate strong positive correlations’. I will be able to find the values of the correlation coefficients by using a CASIO graphical calculator (CFX-9850GC PLUS).

After carrying out the method I explained in the previous hypothesis I found the correlation coefficient of the mental test and the calculator written paper (Paper 2) for the male population to be ‘r = 0.775’ and the correlation coefficient for the female population to be ‘r = 0.698’. Now that I have found the correlation coefficients of the mental test and the calculator written paper

(Paper 2) for the male and female populations I can quite truthfully articulate that my hypothesis ‘the correlation coefficient for the female population will be larger than the correlation coefficient for the male population. Furthermore I again predict the values of the correlation coefficients for both the male and female population to be between 0.5 < r  1, which would indicate strong positive correlations’ was incorrect and erroneous because the correlation coefficient for the male population, which was ‘r = 0.775’ was larger than the correlation coefficient for the female population, which was ‘r = 0.698’. A fraction of my hypothesis that was proved correct was both correlation coefficients that I acquired were in the region of 0.5 < r  1, which would indicate strong positive correlations.

...read more.

This student written piece of work is one of many that can be found in our GCSE Miscellaneous section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related GCSE Miscellaneous essays

  1. Maths Statistics Coursework

    than Key Stage 4's mean (-2.74163), as this is quite unexpected. Unsurprisingly, Key Stage 3's mean is very far off from zero at -6.01616. This means that in fact Key Stage 5's values are closely bunched (due to standard deviation)

  2. The relationship between level of parental education and SAT scores

    to see if there are any significant differences between the test takers' scores and their parents' highest level of education. Using mean values of SAT scores as dependent variables corresponding to levels of parental education as independent variables, several graphs were created.

  1. The aim of the project is to investigate the correlation between multiple sets of ...

    Other than this, the graph should suggest that other methods of travel are more widespread among females, but taking the data into account, it can be concluded that these methods are somewhat equally used by both genders. Hypotheses 1) From the evidence gathered from this basic, at-a-glance analysis, I think

  2. Fixed Point Iteration

    Where x = g(x) method may fail There is also another way to rearrange the equation 1/2lnx + x - 10 = 0. The other rearrangement is x = e2(10-x). Let g(x) = e2(10-x). The graph below shows y = g(x). I will repeat the process above using the same equation.

  1. Mathematics Handling Data Coursework: How well can you estimate length?

    Also, if some saw it from a farther distance than others then it could seem smaller. The experiment, ideally, should have taken place in a classroom and all pupils should have seen it from the same distance. Also, each pupil should have seen it for the same amount of time

  2. maths estimation coursework

    Many factors need to be considered when choosing a suitable area of estimation to investigate. I believe that the main one is that of time consumption, how long these results will take to collect. Estimation of time per person seems very time consuming, and if it were to be done

  1. Statistical Experiment Plan to investigate the ability to estimate 30 and 60 seconds.

    From this I will select the gender sample size starting from the top(so in my example I would select the first 20 numbers in the random sequence). With this sequence I will select the data in the overall gender gender corresponding with my random sequence(in my example the first 20).

  2. Math Investigative Task - calculating the value of metal used in coins.

    5. Current price of copper and zinc (as of 18 October, 2011): 1. Copper: $6.90 per kilogram or $3.1362 per pound 2. Zinc: $1.75 per kilogram or $0.7959 per pound To find out the actual manufacturing value of a coin, I will add the cost of copper and zinc.

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work