Question

The magnitudes and depths of 7 earthquakes are listed below.

Depth 7.0 7.0 7.1 7.1 6.8 7.2 6.9

Magnitude 2.44 1.97 2.32 2.78 1.94 2.40 2.12

(a) Determine the correlation of these two variables.

(b) Generate a scatterplot for these variables. Use depth as the explanatory variable.

(c) In just a sentence or two, explain why it’s appropriate to construct a regression line for this data.

(d) Find the equation of the least-squares regression line. Add the line to your scatterplot

Answer 1

if depth is the explanatory variable then it means it is independent (x) and the magnitude is dependent (y).

	Depth (x)	Magnitude (y)	x ^2	y^2	xy
1	7	2.44	49	5.954	17.08
2	7	1.97	49	3.881	13.79
3	7.1	2.32	50.41	5.382	16.472
4	7.1	2.78	50.41	7.728	19.738
5	6.8	1.94	46.24	3.764	13.192
6	7.2	2.4	51.84	5.760	17.28
7	6.2	2.12	38.44	4.494	13.144
Total	48.4	15.97	335.34	36.9633	110.696
Mean	6.914	2.281

(a) Determine the correlation of these two variables.

Correlation coefficient

(b) Generate a scatterplot for these variables. Use depth as the explanatory variable.

We have the depth values on 'x-axis' and the magnitude values on y-axis. The plot explain a weak positive correlation.

(c) In just a sentence or two, explain why it’s appropriate to construct a regression line for this data.

From the correlation we can say that there is a weak positive but this shows the direction of change in magnitude due to depth not how much the change would be. Using the regression line we can find out how much change in magnitude can be predicted by depth.

(d) Find the equation of the least-squares regression line. Add the line to your scatterplot.

Regression eq of Y on X

slope =

= 0.399

   intercept

= -0.479

For plotting the regression line, one can take 2 random values for 'x' within the range of given values for depth. Using the regression line , 'y' values can be calculated. These points can be plot on the graph and a line passing these points should be drawn.

x	y
6.8	2.236
7.1	2.356

Line can be extended I couldn't due to computerized plot.