Aim #100: How do we create residual plots using our calculator? How do we use a residual plot to determine whether a linear regression model is best to use to describe the relationship between two numerical values?Homework: handoutDo Now: Suppose you were given a scatter plot and least-squares line that looked like this:

Describe what the residual plot would look like.

Using a residual plot provides another indication of the type of relationship between two variables. Consider the scatter plot and line of best fit below.

1) What kind of residual will point A have?

2) What kind of residual will point B have?

3) What kind of residual will point C have?

5-16-17

Using a graphing calculator, we will construct a residual plot . In an earlier lesson, you looked at a data set giving the shoe lengths and heights of twelve adult women. This data set is shown in the table below.

To determine if the linear model is best to describe the relationship between our variables, we examine the residual plot. If the points on the residual plot are randomly scattered, then our relationship is linear.

A pattern in the residual plot indicates that the relationship in the original data set is not linear (for example, the points are curved or u-shaped). The data may be best represented by a quadratic or exponential regression. The residual plot will then have points randomly scattered, indicating that the model chosen was the best choice.

For the following scatterplots, a linear regression was performed. Determine whether this model was the best fit based upon the residual plots shown:

On your calculator:

1) Construct a scatter plot.

2) Construct the line of best fit.

3) Construct the residual plot.

***All instructions are on the last page.***

Water expands as it heats. Researchers measured the volume (in mL) of water at various temperatures. The results are shown below. Using a graphing calculator, construct the scatter plot of this data set. Include the least-squares line on your graph. Make a sketch of this scatter plot, including the least-squares line, on the axes below.

Using a graphing calculator, construct a residual plot for this data set. Make a sketch of the residual plot on the axes given below.

Do you see a clear curve in the residual plot? What does this tell you about the original data set?

Sum it up!-After fitting a line, the residual plot can be constructed using a graphing calculator. -A random scatter of points in the residual plot indicates that the linear function was an appropriate model for the relationship between the bivariate data given. A curve or pattern in the residual plot indicates a non-linear relationship for the original data set.

Construct a scatter plot, line of best fit, and a residual plot using your calculator for the table below. Determine, based upon the residual plot, whether the linear model was the most appropriate model to represent the original data set and explain why.