Question

use the points to describe the data and determine the line of best fit.
what type of correlation do the data points represent?
negative
what is the best estimate for the y - intercept?
<
what is the equation that best represents the data?
<

Explanation:

Step1: Determine the type of correlation

As elevation (x - axis) increases, temperature (y - axis) decreases. So, the correlation is negative.

Step2: Estimate the y - intercept

The y - intercept is the value of y when x = 0. Looking at the scatter plot, if we assume a linear trend and extend the line (mentally), a rough estimate of the y - intercept is around 80.

Step3: Estimate the slope

Let's take two points. Suppose we take a point near (0,80) (estimated y - intercept) and another point. Let's say (800,40). The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Here, \(y_1 = 80,y_2=40,x_1 = 0,x_2 = 800\). Then \(m=\frac{40 - 80}{800-0}=\frac{- 40}{800}=-0.05\)
The equation of a line is \(y=mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. So the equation is \(y=-0.05x + 80\)

Answer:

The type of correlation is negative. The best estimate for the y - intercept is 80. The equation of the line of best fit is \(y=-0.05x + 80\)