Question

Determine the logarithmic regression of the data below using either a calculator or spreadsheet program. Then, estimate the y value when the x value is 10. Round your answer to the nearest tenth. Do not include units in your answer. (1,9),(11,139),(19,200),(28,245),(39,263),(51,299)

Answer 1

Logarithmic equation: y = 3401.5 * (x^1.2722). Estimated y for x=10: 3401.5.

Here is the logarithmic regression of the data and the estimated y value when the x value is 10.

| x | y | log(x) | log(y) |

| 1 | 9 | 0 | 2.20146 |

| 11 | 139 | 2.3979 | 4.95597 |

| 19 | 200 | 2.9444 | 5.3028 |

| 28 | 245 | 3.3322 | 5.51007 |

| 39 | 263 | 3.6375 | 5.56599 |

| 51 | 299 | 3.9318 | 5.70577 |

The equation of the logarithmic regression line is:

log(y) = 2.20146 + 1.2722 * log(x)

Therefore, the estimated y value when the x value is 10 is:

y = exp(2.20146 + 1.2722 * log(10)) ≈ 3401.5