TWMM Unit 2 Reflection

1.  a)  When does it make sense to choose a linear function to model a set of data?

Linear Functions allow you to calculate any X value from a Y, or vice versa. They are commonly easy to find from a graph or table, and can be converted into them. Linear functions are optimal in a position where you have a predictable relation between two or more variables. It is also good for predicting values of variables relative to other variables.

b)  What steps would you follow to find a line of best fit? Include how you would calculate the residuals and what those results might tell you.

One of the easiest ways is simply to eyeball a line into a graph, and then calculate the slope and Y-intercept for it. However, it is also possible to calculate the slope between every two points, and then average the slope, and then use the slope to find the Y-Intercept. To calculate residuals, calculate, using your formula, a Y for each X that has been pre-defined, and then compare it to the pre-defined Ys. If the residuals are high, you probably have an inaccurate equation.

2.  How would you find the equation for a linear function in the following situations?

a)  You are given a description of the variables in words.

Simply put, finding equations in words is a matter of logic. Search for a relation between two values

b)  You are given a table of values for the variables.

Find the slope using the table- find the distance between two different X values, and put that number over the difference between their corresponding Y values. To find the Y-intercept, find the value of Y when X is zero using the slope. Insert all of the values into the equation Y=mx+b

c)  You are given a graph of sample data points.

Find the slope using the graph instead- pick two points, and calculate the rise over run for them to find the slope. The Y-intercept is possible determinable by the graph if it shows where Y crosses over 0- but otherwise, you will need to find Y when X is zero. Place them into the equation Y=mx+b.