Statistics Correlation and Regression - Statistics Assignment Help

Assignment Task

Is quantitative
• Uses a standardised questionnaire or  standardised interview
• Correctly a “survey” is an activity. So when you survey the people, you conduct  research by surveying your study  participants
• A questionnaire is an object/instrument  used in surveys, but you can do many  surveys without a questionnaire
Wording must match target group
• Only one construct per question (a  “construct” refers to an idea or fact)
• Use questions where the ‘right’ answer is  not always in the same place or the same  number
• Use check questions where the same  issue is asked more than once so that  internal reliability can be measured

Regression and correlation
Statistics: Correlation and Regression
This section covers:
•           Correlation coefficient
•           Simple linear Regression
 
Correlation Coefficient
Statistical technique used to measure the strength of linear association between two continuous variables, i.e. the closeness with which points lie along the regression line (see below). The correlation coefficient (r) lies between -1 and +1 (inclusive).
•           If r = 1 or -1, there is perfect positive (1) or negative (-1) linear relationship
•           If r = 0, there is no linear relationship between the two variables
When calculated using the observed data, it is commonly known as Pearson's correlation coefficient (after Karl Pearson who first defined it). When using the ranks of the data, instead of the observed data, it is known as Spearman's rank correlation.
Conventionally
       0.8 ≤ |r| ≤ 1.0            => very strong relationship
       0.6 ≤ |r| < 0.8            => strong relationship
       0.4 ≤ |r| < 0.6            => moderate relationship
       0.2 ≤ |r| < 0.4            => weak relationship
       0.0 ≤ |r| < 0.2            => very weak relationship
…where |r| (read “the modulus of r”) is the absolute (non-negative) value of r.
One can test whether r is statistically significantly different from zero (the value of no correlation). Note that the larger the sample the smaller the value of r that becomes significant. For example, with n=10 paired observations, r is significant if it is greater than 0.63. With n=100 pairs, r is significant if it is greater than 0.20.
The square of the correlation coefficient (r2) indicates how much of the variation in variable y is accounted for (or “explained”) by the variable x. For example, if r = 0.7, then r2 = 0.49, which suggests that 49% of the variation in y is explained by x.
 
Important Points:
•           Correlation only measures linear association. A U-shaped relationship may have a correlation of zero.
•           It is symmetric about the variables x and y - the correlation of (x and y) is the same as the correlation of (y and x).
•           A significant correlation between two variables does not necessarily mean they are causally related.
•           For large samples very weak relationships can be detected.
 

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