As a researcher you will be considering the relationships between variables regu
ID: 3048945 • Letter: A
Question
As a researcher you will be considering the relationships between variables regularly. Linear correlation is the most basic relationship that may exist between two variables. This assignment will you give the opportunity to see how statistics can start to answer the research questions you will be faced with in your field of study.
Correlation Project Directions:
Consider a possible linear relationship between two variables that you would like to explore.
Define the relationship of interest and a data collection technique.
Determine the appropriate sample size and collect the data.
Perform the appropriate analysis to determine if there is a statistically significant linear relationship between the two variables. Describe the relationship in terms of strength and direction.
Construct a model of the relationship and evaluate the validity of that model.
Show all work to receive full credit. Provide complete sentence explanations for each of the above.
Explanation / Answer
In academic field a subject of interest is the linkages between different subjects. Thus, proficiency in math is linked to proficiency in statistics as also economics. As a matter of interest, we could see how theory knowledge impacts practical applications. The scores of 11 students in Statistics Paper 1 (Theory) and Statistics Paper 2 (Practicals) in the final examination are given below: [i represents the student number, xi represents the score in Paper 1 and yi represents the score in Paper 2]
i
1
2
3
4
5
6
7
8
9
10
11
xi
80
45
55
56
58
60
65
68
70
75
85
yi
82
56
50
48
60
62
64
65
70
74
90
Let us assume that y is dependent (response variable) of x (predictor variable) and postulate the model as: y = 0 + 1x + , where is the error term which is assumed to be Normally Distributed with mean 0 and variance 2.
Least square estimates of 0 and 1 are given by:
1cap = Sxy/Sxx and 0cap = Ybar – 1cap.Xbar..……………………………………………..(3)
Mean X = Xbar = (1/n)sum of xi ………………………………………….……………….(4)
Mean Y = Ybar = (1/n)sum of yi ………………………………………….……………….(5)
Sxx = sum of (xi – Xbar)2 …………………………………………………..………………………………..(6)
Syy = sum of (yi – Ybar)2 …………………………………………………..………………………………..(7)
Sxy = sum of {(xi – Xbar)(yi – Ybar)} …………………………………………………………………….………(8)
All above sums are over i = 1, 2, …., n
n = sample size ………………………………………………………………………………(9)
Using Excel the above are computed as below:
1cap = 0.99 and 0cap = 1.02
Thus, estimate of y = 1.02 + 0.99x.
As an illustration, a student with a score of 60 in Paper 1 is expected to get a score of 60.42 [1.02 + (0.99 x 60)] in Paper 2.
DONE
i
1
2
3
4
5
6
7
8
9
10
11
xi
80
45
55
56
58
60
65
68
70
75
85
yi
82
56
50
48
60
62
64
65
70
74
90
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