Review the chapter readings of this week and assess the following concepts:
- When is the chi-squared statistic used in testing hypotheses? Include underlying assumptions and the test statistic for testing hypotheses on a single population variance.
- What is a correlation coefficient? What is the range of its possible values, and why?
- How do you determine if a correlation coefficient is statistically significant?
- In a simple regression, what is the coefficient of determination, and how is it interpreted?
- Peer response:
- The correlation coefficient is a statistical measure of how strong a relationship exists between two variables’ relative movements. The range of possible values for a good correlation coefficient is between negative 1.0 and a positive 1.0. Values close to -1.0 are said to have a strong negative relation while those close to 1.o have a strong positive relationship (Darlington & Hayes, 2016). Values at zero or close to it denotes a weak or no linear relationship. The reason as to why the range of values should remain within the range limit is that anything outside it will be interpreted as having an error in correlation coefficient.
A correlation coefficient is said to be statistically significant if ‘r’ is not found between the negative and positive critical values (Darlington & Hayes, 2016). Similarly, a correlation coefficient is said to be statistically significant if the p-value or the significance level of the correlation can be determined by using the correlation coefficient table for the degrees of freedom. For instance, df=n-2, where n is the number of observations in x and y variables.
In simple regression analysis, the coefficient of determination, denoted by R^2, is a measure in statistic that tests how a model projects or explains an outcome in a linear regression (Darlington & Hayes, 2016). It signifies how well the regression model fits the observed data. It is interpreted as the proportion in the dependent variable that is forecastable from the independent variable.Reference
Darlington, R. B., & Hayes, A. F. (2016). Regression Analysis and Linear Models: Concepts, Applications, and Implementation. In Google Books. Guilford Publications. https://books.google.co.ke/books?hl=en&lr=&id=YDgo…
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