Question

Type the correct answer in each box. Round your answers to the nearest tenth. The table shows the heights of three different rock formations that Jeremy is considering. Use the line of best fit to predict how long it will take to climb and come back down the three rock formations.

Answer 1

Answer:

The line of best fit is: y = -4.883 + 0.395·x

Step-by-step explanation:

The data provided is:

Time (in min.) Height (ft.)

      30             85

      45            120

     115            298

      87            194

     160            434

      60            241

     135            351

     117            339

      55            180

     145            400

      95            248

     150            370

      67            155

     120            296

     100            271

      88            255

     138            315

      75            215

     167            405

     120            317

In this case we need to form the line of best fit to predict how long it will take to climb and come back down the three rock formations.

So, the dependent variable is the time and the independent variable is the height.

The general form of the line of best fit is:

y = a + b·x

Compute the values of a and b as follows:

$a=\frac{\sum Y\cdot\sum X^{2}-\sum X\cdot\sum XY}{n\cdot\sum X^{2}-(\sum X)^{2}}=\frac{2069\cdot 1683499-5489\cdot637721}{20\cdot1683499-(5489)^{2}}=-4.883\\\\b=\frac{n\cdot\sum XY-\sum X\cdot\sum Y}{n\cdot\sum X^{2}-(\sum X)^{2}}=\frac{20\cdot 637721-5489\cdot2069}{20\cdot1683499-(5489)^{2}}=0.395$

Thus, the line of best fit is:

y = -4.883 + 0.395·x