# Non-Linear Scatterplot

See the attached file.

An experiment is conducted to determine the relationship between initial speed and stopping distance of automobiles. A sample of twelve cars is tested and the following data are recorded:

Initial speed in mph (x) 20 20 30 30 40 40 50 50 60 60 70 70

Stopping distance in ft (y) 15.9 24 41.2 58.7 74.8 88.8 112.6 127.6 216.4 200 276.8 301

1. Draw the scatterplot of this data. Observe that the shape is not linear. How can you best describe the shape?

2. Create a new set of data using the transformation y' = sqrt(y). In other in the above table keep the x values the same and replace the y values by y' values.

3. Draw a scatterplot of this data. What can you say about the shape of this scatterplot?

4. Find the linear equation that best describes the relationship between x and y'

5. Replace the y' in this equation by sqrt(y) and solve the resulting equation for y.

6. Write a brief conclusion.

https://brainmass.com/math/linear-transformation/nonlinear-scatterplot-517557

#### Solution Preview

1) Based on the scatter plot on the left, it is not linear. To some extent, it is like inverted half bell shape.

2,3) After this transformation, we could see that the shape is linear line. ...

#### Solution Summary

The solution assists with creating a non-linear scatterplot.

Scatter Plots, Pearson's Correlation, Regresssion

Question 1

Show us a scatterplot between two interval level variables. (Use Excel to chart them.) Are the results bunched together or far apart? Is the relationship linear? Is the relationship non-linear? Is there no apparent relationship between the two variables?

Question 2

We use Pearson's correlation coefficient as a measure of association between 2 continuous variables. Give some examples of where two concepts (variables) are correlated, but this does not imply a causal relationship between the two. Can there be a causal relationship between two items but no correlation?

Question 3

Find a study with regression in it. Report on the model (the regression coefficient and the R-squared) and interpret the results. By how much does the dependent variable change for a one-unit change in the independent variable? Is the coefficient significant (i.e., is its t-score close to 2 or above, or does it have a p-value less than .05)?