Question

state if there appears to be a positive correlation, negative correlation,
there is a correlation, find the slope - intercept form of the equation of
data.

1. \\( \

$$\begin{array} { l l } { x } & { y } \\\\ \\hline 30 & { 4 } \\\\ 110 & { 3.6 } \\\\ 270 & { 3 } \\\\ 280 & { 3.1 } \\\\ \\hline \\end{array}$$

\\) \\( \

$$\begin{array} { l l } { x } & { y } \\\\ \\hline 310 & { 3.2 } \\\\ 350 & { 2.6 } \\\\ 410 & { 2.6 } \\\\ \\hline \\end{array}$$

\\) \\( \

$$\begin{array} { l l } { x } & { y } \\\\ \\hline 580 & { 2 } \\\\ 950 & { 0.9 } \\\\ 960 & { 0.9 } \\\\ \\hline \\end{array}$$

\\)

Explanation:

Step1: Determine the type of correlation

Looking at the scatter - plot, as \(x\) (the independent variable) increases, \(y\) (the dependent variable) generally decreases. So, there is a negative correlation.

Step2: Select two points for the slope calculation

Let's take two points \((x_1,y_1)=(30,4)\) and \((x_2,y_2)=(960,0.9)\)
The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\)

$$m=\frac{0.9 - 4}{960 - 30}=\frac{- 3.1}{930}\approx - 0.0033$$

Step3: Use the point - slope form \(y - y_1=m(x - x_1)\)

Using the point \((x_1,y_1)=(30,4)\) and \(m\approx - 0.0033\)

$$y - 4=-0.0033(x - 30)$$

$$y-4=-0.0033x+0.099$$

$$y=-0.0033x + 4.099$$

Answer:

There is a negative correlation. The slope - intercept form of the equation (approximate) is \(y=-0.0033x + 4.099\)