# Case III - Linear relationship

Description of activity and Excel instructions:Case III - Linear relationship

Dataset: baby-crying-IQ.xls

## Contents

## Exploratory data analysis

### Create a scatterplot

Use the *Chart Wizard* to create a scatterplot.

- Select the columns containing the two variables to be plotted.
- Select
**Insert**>**Chart...**.

The *Chart Wizard* displays.

In *1. Chart Type*:

- Select
**XY (Scatter)**. - Select the
**Points Only**version.

In *2. Data Range*:

- Click '
*Data series in columns*. - Check
**First row as label**.

No changes are needed for *3. Data Series*.

In *4. Chart Elements*:

- Enter a title for the chart.
- Enter a title for the X axis (explanatory variable).
- Enter a title for the Y axis (response variable).
- Decide if you want to display a grid in the chart background.
- Uncheck the
*Display Legend*box.

Calc creates a scatterplot. Note that the X axis scale is shown as 5 to 35, a reasonable choice for this data.

If you want to change the shape or size of the data points:

- Double click on the graph to enter edit mode.
- Right click on the data points.
- Select
**Object Properties...** - Explore the options in the
*Icon*section, in the*Line*tab.

### Create a correlation coefficient

Use a formula to compute the correlation:

- Click in a cell outside of the first two columns of data.
- Type "=CORREL([range1],[range2])" where [range1] is the first column of data and [range2] is the second column of data.

Return to the OLI's Case III - Linear relationship page to complete the first interpretive exercise.

## Calculate p-value

Calc does not include a formula or data analysis routine to calculate the "t-test for the slope" of a regression line. You can use Excel for this activity, or the web-based p-value calculator for the correlation coefficients at danielsoper.com.

In fact, this t-test is solely dependent on the value of the correlation coefficient, r, and the size of the sample:

- [math]t = \frac{r}{\sqrt{\frac{1-r^2}{n-2}}}[/math]

Return to the OLI's Case III - Linear relationship page to complete the next interpretive exercise.

## Plot the least squares regression line

- In edit mode on the graph, right-click one of the points on the graph.
- Select
**Insert Trend Line...**.

The *Trend Line* dialog displays.

- Click on the
**Type**tab. - Verify that
**Linear**is selected under*Regression Type*. - Check the
**Show equation**box. - Check the
**Show correlation coefficient (R**.^{2}) - Click
**OK**.

The regression line displays among the data points and the regression equation and R^{2} display underneath. You can select and re-position the equation and R^{2} value, if they are displayed on top of the data points.

Return to the OLI's Case III - Linear relationship page to complete the interpretive exercises.