For the following data:

x |
1.4 |
2.4 |
4.0 |
4.9 |
5.7 |
6.3 |
78 |
90 |
9.3 |
11.0 |

y |
2.3 |
3.7 |
5.7 |
9.9 |
6.9 |
15.8 |
15.4 |
36.9 |
34.6 |
53.2 |

a. Make a scatterplot of y versus x. Is the relationship between x and y approximately linear, or is it nonlinear?

b. Compute the natural logarithm of each y value. This is known as making a log transformation of y. Make a scatterplot of In y versus x. Is the relationship between x and In y approximately linear, or is it nonlinear?

c. In general, it is easier to work with quantities that have an approximate linear relationship than with quantities that have a nonlinear relationship. For these data, do you think it would be easier to work with x and y or with .t and In y? Explain.

Answer:

Step 1 of 4:

The given data is

x |
1.4 |
2.4 |
4 |
4.9 |
5.7 |
6.3 |
7.8 |
9.0 |
9.3 |
11.0 |

y |
2.3 |
3.7 |
5.7 |
9.9 |
6.9 |
15.8 |
15.4 |
36.9 |
34.6 |
53.2 |

Step 2 of 4:

a). We need to make a scatter plot of y versus x.

We observe the above scatter plot, we conclude that the relationship is nonlinear.