# week 10.2 discussion response

**Write a response to each discussion post.**

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**Sperry 10.2**

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The Pearson correlation is to summarize the relationship between two variables as a single number, and the coefficient of determination indicates what proportion of the variance in one of the variables is associated with the variance in the other variable. For example, I state coat sales increase with dropping temperatures. To prove this I would gather data on sales and temperatures for those days. Next, I would plot this information and would see that the linear relationship is strong. Then I would calculate the Pearson correlation and the coefficient of determination (Erford, 2015).

Linear regression tries to explain the relationship between the two variables by fitting the linear equation into observed data. The linear regression tells the strength of the effect that the independent variable have on the dependent variable. It can also be used to make predictions. Take my example of coat sales, due to global warming coat sales will slowly decrease (Erford, 2015).

Partial correlation measures association between two variables, while at the same time it controls the effects of a third variable. For example, in April there is always a spike in sales when the average temperature is 42 degrees, because the third controlled variable would the end of season sales. The Semipartial correlation removes the effects of additional variables from one of the variables that were included.

**Pomajzl 10.2**

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The Pearson product-moment correlation coefficient summarizes the relationship between two variables as a single number. It is able to take values with a positive “r” indicating a positive linear relationship and values with a negative “r” indicating a negative linear relationship (Erford, p. 363). The decimal indicated the strength of the relationship, meaning the closer the absolute value of “r” to 1, the stronger the correlation is (Erford, p. 363). The easiest way to explain this and determine this is using a scatterplot. The closer the plots are to creating a straight line determines the indication of a stronger relationship.

The coefficient of determination is the square of the correlation coefficient, which indicates the ratio of the modification in one of the variables, is associated with the modification of the other variable. (Erford, p. 371).

The linear relationship between two variables can be used to predict the value between two variables (Erford, p. 375). For example, if the amount of x is used to predict the amount of y, then the amount of y is used to predict the amount of x. They rely on each other.

The elements of linear regression are the slope and intercept. The slope tells the steepness and the intercept is the predicted value of the regression line.

Partial correlation is when the effect of a third variable is removed (Erford, p. 375). Partial correlation only occurs when two variables are correlated because of the third variable in which they are both linked.

A semipartial correlation occurs when three variables have an effect on one another in some form or way however, it may not be direction. For example, ‘x’, ‘y’, ‘z’ are all in the same study. However ‘x’ and ‘y’ correlate and ‘x’ and ‘z’ correlation but, ‘y’ and ‘z’ are partialled out because they do not coordinate with one another (Erford, p. 381).

Partial correlation and semi partial correlation are similar because they both contain three variables and the one of the variables is removed in some form whether it be completely removed or just partially removed with two variables, which do not coordinate.

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