Is the magnitude of an earthquake related to the depth below the surface at whic

Question

Is the magnitude of an earthquake related to the depth below the surface at which the quake occurs? Let x be the magnitude of an earthquake (on the Richter scale), and let y be the depth (in kilometers) of the quake below the surface at the epicenter. x 3.0 4.6 3.3 4.5 2.6 3.2 3.4 y 5.2 10.1 11.2 10.0 7.9 3.9 5.5 b) Find x, y, b, and the equation of the least squares line. x = 3 Correct: Your answer is correct. y = 17.54 Correct: Your answer is correct. b = ? = (c) Find the sample correlation coefficient r and the coefficient of determination r?2. (Round your answers to three decimal places.) r = r?2 = What percentage of variation in y is explained by the least-squares model? (Round your answer to one decimal place.) % Need Help? Read It

Explanation / Answer

Using Minitab:

Click Stat > Regression > Regression

Regression Analysis: Y versus X

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value
Regression 1 13.06 13.058 1.82 0.235
X 1 13.06 13.058 1.82 0.235
Error 5 35.81 7.162
Total 6 48.87

Model Summary

S R-sq R-sq(adj) R-sq(pred)
2.67623 26.72% 12.06% 0.00%

Coefficients

Term Coef SE Coef T-Value P-Value VIF
Constant 0.81 5.19 0.16 0.883
X 1.96 1.45 1.35 0.235 1.00

Regression Equation

Y = 0.81 + 1.96 X

least squares line when x = 3

Y = 0.81 + 1.96 *3=6.69

Correlation :

correlation of X and Y =r = 0.517

There is positive Correlation between two variables.

r?2 = What percentage of variation in y is explained by the least-squares model = 26.72%

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.