Question

A stonemason wants to look at the relationship between the density of stones she cuts and the depth to which her abrasive water jet cuts them. The data show a linear pattern with the summary statistics shown below:
Find the equation of the least-squares regression line for predicting the cutting depth from the density of the stone.
Round your entries to the nearest hundredth.

Answer 1

Answer:

The equation is ; ŷ = 374.20 +  (- 133)$x$

Step-by-step explanation:

In this question, we are tasked with finding the equation of least-squares regression line using the data available in the question.

Mathematically, the equation of a staright line is y = mx + c; where m is the slope of the line and c is the y-intercept of the line.

We proceed with the question as follows;

To find the slope of the line, the formula to use is;

slope = r × $\frac{s_{y} }{s_{x} }$  = -0.95 × 42/0.3 = -133

Now, we proceed to calculate the y-intercept. This is quite easy as we have the vale of the slope already;

From y= mx + c

c = y - mx;  41.7 - (-133 × 2.5) = 374.20

Thus, the equation of the regression line is;

ŷ = 374.20 + (- 133)$x$