Question

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1. How might you use a trend line to make a prediction about an outcome? Identify the variables and explain the rationale for using the trend line to predict the outcome.

2.  a scenario where the Spearman correlation would be appropriate to use in calculating the strength of the relationship between two variables. Identify the variables and explain the rationale for your answer. What makes this scenario different from the scenario in the previous question?

Answer 1

(1)

A trend line is an equation that describes the relationship between two variables.

The equation for a linear relationship between independent variale (x) and dependent vaiable (y) is given by:

y = ax + b,

where a is the slope and b is the y - intercept.

By giving values to x, we can get the predicted value of y.

The prediction about an outcome is correct if the independent variable chosen for prediction is within the interval in which it is defined. This is called interpolation. Any value beyond the defined interval is extrapolation and prediction with extrapolation may not yield accurate value.

(2)

Spearman's Rank - Order Correlation would be appropriate to use in calculating the strength of the relationship between two variables: independent variable (x) and dependent variable (y) in scenerios when the exact values of x and y are not kown but their ranks are known. The Spearman's Rank - Order Correlation is the non-parametric version of the Peason's Product Moment Correlation. This scenerio is different from the scenerio in the previous question in that in making prediction about an outcome, we assume that a linear relation exists between x and, while Spearman's Correlation is to obtain a value from which we can assess whether linear relationship exists between x and y and how strong is the relationship.